10 124 Quick Notes - Revision history

Rosslahaye at 19:36, 2 December 2024

2024-12-02T19:36:57Z

← Older revision		Revision as of 15:36, 2 December 2024
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	[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).		[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).

	It seems like the prior statement is incorrect. I suspect what this should say is [[10_124]] and [[8_19]] are the only torus knots which are also almost alternating. See page 108 in the Encyclopedia of Knot Theory. Confirmation of this is that [[3_1]] is the pretzel knot (1,1,1), i.e., the right-handed trefoil. It looks like [[5_1]] is a pretzel knot also, and so on. These are torus knots also.		It seems like the prior statement is incorrect. I suspect what this should say is [[10_124]] and [[8_19]] are the only torus knots which are also almost alternating. See page 108 in the Encyclopedia of Knot Theory. Confirmation of this is that [[3_1]] is the pretzel knot P(1,1,1), i.e., the right-handed trefoil. It looks like [[5_1]] is a pretzel knot also, and so on, i.e. [[7_1]], [[9_1]], and should include the Hopf link and the Solomon link etc. These are torus knots/links also.

2024-12-02T19:33:04Z

Possible correction to a claim

← Older revision		Revision as of 15:33, 2 December 2024
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	[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).		[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).

			It seems like the prior statement is incorrect. I suspect what this should say is [[10_124]] and [[8_19]] are the only torus knots which are also almost alternating. See page 108 in the Encyclopedia of Knot Theory. Confirmation of this is that [[3_1]] is the pretzel knot (1,1,1), i.e., the right-handed trefoil. It looks like [[5_1]] is a pretzel knot also, and so on. These are torus knots also.

2008-12-19T11:24:52Z

Reverted edits by TrdelLarac (Talk); changed back to last version by Drorbn

← Older revision		Revision as of 07:24, 19 December 2008
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	lioloa
	[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).		[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).

2008-12-19T10:06:05Z

rolicdarlaz

← Older revision		Revision as of 06:06, 19 December 2008
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			lioloa
	[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).		[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).

2007-11-29T00:32:59Z

← Older revision		Revision as of 20:32, 28 November 2007
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	~~Also~~ known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).		[[10_124]] is also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).

2005-11-07T01:53:34Z

← Older revision		Revision as of 21:53, 6 November 2005
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			Also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).
	Also known as "The Torus Knot [[T(5,3)]]".

2005-10-18T13:31:33Z

← Older revision		Revision as of 09:31, 18 October 2005
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	Also known as "The Torus Knot [[T(5,3)]]".		Also known as "The Torus Knot [[T(5,3)]]".

	If one takes the symmetric diagram for 10_123 and makes it doubly alternating one gets a diagram for 10_124. That's the torus knot view. There is then a nice representation of the quandle of 10_124 into the dodecahedral quandle Q_30. See http://www.maths.warwick.ac.uk/~bjs/add233.html

2005-10-18T13:23:50Z

← Older revision		Revision as of 09:23, 18 October 2005
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	Also known as "The Torus Knot [[T(5,3)]]".		Also known as "The Torus Knot [[T(5,3)]]".

			If one takes the symmetric diagram for 10_123 and makes it doubly alternating one gets a diagram for 10_124. That's the torus knot view. There is then a nice representation of the quandle of 10_124 into the dodecahedral quandle Q_30. See http://www.maths.warwick.ac.uk/~bjs/add233.html

2005-08-31T07:01:41Z

New page

Also known as "The Torus Knot [[T(5,3)]]".