AKT-09/HW3 - Revision history

Drorbn at 23:36, 23 November 2009

2009-11-23T23:36:00Z

← Older revision		Revision as of 19:36, 23 November 2009
Line 1:		Line 1:
	{{AKT-09/Navigation}}		{{AKT-09/Navigation}}

	'''Solve the following problems''' and submit them in class by ~~November~~ 24, 2009:		'''Solve the following problems''' and submit them in class by December 1, 2009:

	'''Problem 1''' With <math>T</math>, <math>B^+</math> and <math>R</math> as below, write <math>B^+</math> as a composition of <math>T</math> and two <math>R</math>'s, using he basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math>.		'''Problem 1''' With <math>T</math>, <math>B^+</math> and <math>R</math> as below, write <math>B^+</math> as a composition of <math>T</math> and two <math>R</math>'s, using he basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math>.

Drorbn at 23:11, 16 November 2009

2009-11-16T23:11:54Z

← Older revision		Revision as of 19:11, 16 November 2009
Line 1:		Line 1:
	{{AKT-09/Navigation}}		{{AKT-09/Navigation}}
	{{In Preparation}}

	'''Solve the following problems''' and submit them in class by November 24, 2009:		'''Solve the following problems''' and submit them in class by November 24, 2009:
Line 6:		Line 5:
	'''Problem 1''' With <math>T</math>, <math>B^+</math> and <math>R</math> as below, write <math>B^+</math> as a composition of <math>T</math> and two <math>R</math>'s, using he basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math>.		'''Problem 1''' With <math>T</math>, <math>B^+</math> and <math>R</math> as below, write <math>B^+</math> as a composition of <math>T</math> and two <math>R</math>'s, using he basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math>.

		⚫	<center>[[Image:AKT-09-TBR.png\|480px]]</center>
⚫	'''Problem 2''' Show that the "topological boundary" operator <math>\partial_T</math> and the "crossing change" operator <math>x_T</math> of the class of November 5 are compositions of the basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math> (you are also allowed to use "nullary" operations, otherwise known as "constants").

		⚫	'''Problem 2''' Show that the "topological boundary" operator <math>\partial_T</math> and the "crossing change" operator <math>x_T</math> of the class of November 5 are compositions of the basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math> (you are also allowed to use "nullary" operations, otherwise known as "constants").
⚫	'''Problem 3''' Write the third Reidemeister move R3 as a relation on <math>Z(B_+)</math>~~, where <math>B_+</math> is given by the picture below:~~

		⚫	'''Problem 3''' Write the third Reidemeister move R3 as a relation on <math>Z(B_+)</math>.
⚫	<center>[[Image:06-~~1350~~-~~BPlus~~.~~svg~~]]</center>

Drorbn at 22:58, 16 November 2009

2009-11-16T22:58:36Z

← Older revision		Revision as of 18:58, 16 November 2009
Line 4:		Line 4:
	'''Solve the following problems''' and submit them in class by November 24, 2009:		'''Solve the following problems''' and submit them in class by November 24, 2009:

	'''Problem 1''' ~~Show~~ ~~that the "topological boundary" operator~~ <math>~~\partial_T~~</math> and ~~the~~ ~~"crossing~~ ~~change"~~ ~~operator~~ <math>~~x_T~~</math> of ~~the~~ ~~class~~ of ~~November~~ 5 ~~are~~ ~~compositions~~ of ~~the~~ basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math>.		'''Problem 1''' With <math>T</math>, <math>B^+</math> and <math>R</math> as below, write <math>B^+</math> as a composition of <math>T</math> and two <math>R</math>'s, using he basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math>.

			'''Problem 2''' Show that the "topological boundary" operator <math>\partial_T</math> and the "crossing change" operator <math>x_T</math> of the class of November 5 are compositions of the basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math> (you are also allowed to use "nullary" operations, otherwise known as "constants").
⚫	'''Problem 2''' Write the third Reidemeister move R3 as a relation on <math>Z(B_+)</math>, where <math>B_+</math> is given by the picture below:

		⚫	'''Problem 3''' Write the third Reidemeister move R3 as a relation on <math>Z(B_+)</math>, where <math>B_+</math> is given by the picture below:

	<center>[[Image:06-1350-BPlus.svg]]</center>		<center>[[Image:06-1350-BPlus.svg]]</center>

Drorbn at 00:00, 10 November 2009

2009-11-10T00:00:53Z

New page

{{AKT-09/Navigation}}
{{In Preparation}}

'''Solve the following problems''' and submit them in class by November 24, 2009:

'''Problem 1''' Show that the "topological boundary" operator <math>\partial_T</math> and the "crossing change" operator <math>x_T</math> of the class of November 5 are compositions of the basic TG operations <math>d_e</math>, <math>u_e</math>, and <math>\#</math>.

'''Problem 2''' Write the third Reidemeister move R3 as a relation on <math>Z(B_+)</math>, where <math>B_+</math> is given by the picture below:

<center>[[Image:06-1350-BPlus.svg]]</center>