0708-1300/Homework Assignment 2 - Revision history

Franklin: /* Just for Fun */

2007-10-07T02:35:49Z

Just for Fun

← Older revision		Revision as of 22:35, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with ~~lots~~ of help from [http://www.maths.ex.ac.uk/~mwatkins/lensspaces.pdf M.Watkins] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with '''LOTS''' of help from [http://www.maths.ex.ac.uk/~mwatkins/lensspaces.pdf M.Watkins] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:34:25Z

Just for Fun

← Older revision		Revision as of 22:34, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [http://www.maths.ex.ac.uk/~mwatkins/lensspaces.pdf\|M.Watkins] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [http://www.maths.ex.ac.uk/~mwatkins/lensspaces.pdf M.Watkins] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:33:48Z

Just for Fun

← Older revision		Revision as of 22:33, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [~~[M. Watkins~~:~~0708-1300lensspaces~~.pdf]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [http://www.maths.ex.ac.uk/~mwatkins/lensspaces.pdf\|M.Watkins] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:29:27Z

Just for Fun

← Older revision		Revision as of 22:29, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[0708-1300lensspaces.pdf~~:M. Watkins~~]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[M. Watkins:0708-1300lensspaces.pdf]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:29:08Z

Just for Fun

← Older revision		Revision as of 22:29, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[0708-1300lensspaces.pdf \|M. Watkins]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[0708-1300lensspaces.pdf:M. Watkins]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:28:35Z

Just for Fun

← Older revision		Revision as of 22:28, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[0708-1300lensspaces.pdf\|M. Watkins]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[0708-1300lensspaces.pdf \|M. Watkins]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:27:40Z

Just for Fun

← Older revision		Revision as of 22:27, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[0708-~~1300-lensspaces~~.pdf\|M. Watkins]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[0708-1300lensspaces.pdf\|M. Watkins]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:25:49Z

Just for Fun

← Older revision		Revision as of 22:25, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[~~M. Watkins\|~~0708-1300-lensspaces.pdf]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[0708-1300-lensspaces.pdf\|M. Watkins]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:25:28Z

Just for Fun

← Older revision		Revision as of 22:25, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[M. Watkins:0708-1300-lensspaces.pdf]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[M. Watkins\|0708-1300-lensspaces.pdf]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.

Franklin: /* Just for Fun */

2007-10-07T02:25:16Z

Just for Fun

← Older revision		Revision as of 22:25, 6 October 2007
Line 27:		Line 27:
	Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?		Prove that the lens space <math>L(3,1</math>), defined in class and on pages 85-86 of our text, can also be obtained by gluing two solid tori <math>D^1\times S^1</math> using a map <math>\varphi:S^1\times S^1\to S^1\times S^1</math> which identifies their (toroidal) boundaries. With the boundaries identified as <math>S^1\times S^1=T^2={\mathbb R}^2/{\mathbb Z}^2</math>, can you write a simple formula for <math>\varphi</math>?

	Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[M. Watkins:0708-~~1300lensspaces~~.pdf]]. So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.		Don't click on the next link if you don't want to see a [[0708-1300/proposed solution\|proposed solution]]. The proposer of this solution did not derive it from the definition on pages 85-85 of our text but from the one in page 151 and with lots of help from [[M. Watkins:0708-1300-lensspaces.pdf]] . So, there is Double-Fun deriving it directly from those formulas in <math>\mathbb{R}^6</math>.