Ukraine Canada Summer School 2006 Talk I - Revision history

Drorbn at 16:47, 5 December 2007

2007-12-05T16:47:44Z

← Older revision		Revision as of 12:47, 5 December 2007
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	* Is the {{KAT Link\|3_1\|trefoil knot}} really knotted?		* Is the {{KAT Link\|3_1\|trefoil knot}} really knotted?
	* Is the trefoil knot equivalent to its mirror image?		* Is the trefoil knot equivalent to its mirror image?
	* Are {{KAT Link\|~~wiki/~~K11n34\|K11n34}} (the "Conway" knot) and {{KAT Link\|K11n42\|K11n42}} (the "Kinoshita-Terasaka" knot) really different?		* Are {{KAT Link\|K11n34\|K11n34}} (the "Conway" knot) and {{KAT Link\|K11n42\|K11n42}} (the "Kinoshita-Terasaka" knot) really different?
	{\| align=center		{\| align=center
	\|-		\|-

Drorbn at 16:46, 5 December 2007

2007-12-05T16:46:45Z

← Older revision		Revision as of 12:46, 5 December 2007
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	Also see ~~[http://www.math.toronto.edu/~drorbn/~~classes/0102/FeynmanDiagrams/NonObvious/index.html Some Non Obvious Examples].		Also see {{Home Link\|classes/0102/FeynmanDiagrams/NonObvious/index.html\|Some Non Obvious Examples}}.

	===Questions===		===Questions===

	* Is the ~~[http://katlas.math.toronto.edu/wiki/3_1~~ trefoil knot] really knotted?		* Is the {{KAT Link\|3_1\|trefoil knot}} really knotted?
	* Is the trefoil knot equivalent to its mirror image?		* Is the trefoil knot equivalent to its mirror image?
	* Are ~~[http://katlas.math.toronto.edu/~~wiki/K11n34 K11n34] (the "Conway" knot) and ~~[http://katlas.math.toronto.edu/wiki/~~K11n42 K11n42] (the "Kinoshita-Terasaka" knot) really different?		* Are {{KAT Link\|wiki/K11n34\|K11n34}} (the "Conway" knot) and {{KAT Link\|K11n42\|K11n42}} (the "Kinoshita-Terasaka" knot) really different?
	{\| align=center		{\| align=center
	\|-		\|-
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	* Can you make a list of all knots?		* Can you make a list of all knots?
	* The trefoil knot is bounds a Seifert surface. Do all knots do?		* The trefoil knot is bounds a Seifert surface. Do all knots do?
	* The complement of the trefoil knot is "fibered" with Seifert surfaces (see ~~[http://www.math.toronto.edu/~drorbn/~~People/BarringtonLeigh/FiberedKnot.html animation]). Is that true for all knots? How does one decide?		* The complement of the trefoil knot is "fibered" with Seifert surfaces (see {{Home Link\|People/BarringtonLeigh/FiberedKnot.html\|animation}}). Is that true for all knots? How does one decide?
	* Which knots are ribbon knots?		* Which knots are ribbon knots?
	* Which knots are slice knots?		* Which knots are slice knots?

Drorbn at 16:59, 15 August 2006

2006-08-15T16:59:37Z

← Older revision		Revision as of 12:59, 15 August 2006
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			Also see [http://www.math.toronto.edu/~drorbn/classes/0102/FeynmanDiagrams/NonObvious/index.html Some Non Obvious Examples].

	===Questions===		===Questions===

Drorbn at 16:48, 15 August 2006

2006-08-15T16:48:27Z

← Older revision		Revision as of 12:48, 15 August 2006
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	* The trefoil knot is bounds a Seifert surface. Do all knots do?		* The trefoil knot is bounds a Seifert surface. Do all knots do?
	* The complement of the trefoil knot is "fibered" with Seifert surfaces (see [http://www.math.toronto.edu/~drorbn/People/BarringtonLeigh/FiberedKnot.html animation]). Is that true for all knots? How does one decide?		* The complement of the trefoil knot is "fibered" with Seifert surfaces (see [http://www.math.toronto.edu/~drorbn/People/BarringtonLeigh/FiberedKnot.html animation]). Is that true for all knots? How does one decide?
	* Which knots are ~~boundary~~ knots?		* Which knots are ribbon knots?
	* Which knots are slice knots?		* Which knots are slice knots?
	* And always, the hardest and most important question in mathematics: '''Why should we care??'''		* And always, the hardest and most important question in mathematics: '''Why should we care??'''

Drorbn at 16:44, 15 August 2006

2006-08-15T16:44:05Z

← Older revision		Revision as of 12:44, 15 August 2006
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	\|}		\|}
	* Which of these two is the knot at the gate of the Cambridge University maths department?		* Which of these two is the knot at the gate of the Cambridge University maths department?
			{\| align=center
⚫	[[Image:Gateknot-negated.jpg\|400px~~\|center~~]]
			\|-
		⚫	\|[[Image:Gateknot-negated.jpg\|400px]]
			\|}
	* Can you make a list of all knots?		* Can you make a list of all knots?
	* The trefoil knot is bounds a Seifert surface. Do all knots do?		* The trefoil knot is bounds a Seifert surface. Do all knots do?

Drorbn at 16:43, 15 August 2006

2006-08-15T16:43:08Z

← Older revision		Revision as of 12:43, 15 August 2006
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	* Is the trefoil knot equivalent to its mirror image?		* Is the trefoil knot equivalent to its mirror image?
	* Are [http://katlas.math.toronto.edu/wiki/K11n34 K11n34] (the "Conway" knot) and [http://katlas.math.toronto.edu/wiki/K11n42 K11n42] (the "Kinoshita-Terasaka" knot) really different?		* Are [http://katlas.math.toronto.edu/wiki/K11n34 K11n34] (the "Conway" knot) and [http://katlas.math.toronto.edu/wiki/K11n42 K11n42] (the "Kinoshita-Terasaka" knot) really different?
			{\| align=center
			\|-
			\|[[Image:K11n34.png]]
			\|[[Image:K11n42.png]]
			\|}
	* Which of these two is the knot at the gate of the Cambridge University maths department?		* Which of these two is the knot at the gate of the Cambridge University maths department?
			[[Image:Gateknot-negated.jpg\|400px\|center]]
	* Can you make a list of all knots?		* Can you make a list of all knots?
	* The trefoil knot is bounds a Seifert surface. Do all knots do?		* The trefoil knot is bounds a Seifert surface. Do all knots do?

Drorbn at 16:31, 15 August 2006

2006-08-15T16:31:00Z

New page

===Questions===

* Is the [http://katlas.math.toronto.edu/wiki/3_1 trefoil knot] really knotted?
* Is the trefoil knot equivalent to its mirror image?
* Are [http://katlas.math.toronto.edu/wiki/K11n34 K11n34] (the "Conway" knot) and [http://katlas.math.toronto.edu/wiki/K11n42 K11n42] (the "Kinoshita-Terasaka" knot) really different?
* Which of these two is the knot at the gate of the Cambridge University maths department?
* Can you make a list of all knots?
* The trefoil knot is bounds a Seifert surface. Do all knots do?
* The complement of the trefoil knot is "fibered" with Seifert surfaces (see [http://www.math.toronto.edu/~drorbn/People/BarringtonLeigh/FiberedKnot.html animation]). Is that true for all knots? How does one decide?
* Which knots are boundary knots?
* Which knots are slice knots?
* And always, the hardest and most important question in mathematics: '''Why should we care??'''

===Some Answers===

* 3-colourings.
* The Kauffman bracket and the Jones polynomial.