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Topic: Torsor

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Homogeneous space

Tangent bundle

	torsors
		We can express this in terms of torsors as follows: relative phases lie in the group of unit complex numbers, which is called U(1), but phases themselves do not: they lie in a "U(1)-torsor".
		The main reason torsors seem subtle is that they correct a bad habit that's deeply ingrained in all of us.
		So, the idea of torsors is to avoid pretending something is a group when it doesn't come naturally equipped with an identity element.
	math.ucr.edu /home/baez/torsors.html (2363 words)

	Principal homogeneous space - Wikipedia, the free encyclopedia
		If G is nonabelian then one must distinguish between left and right torsors according to whether the action is on the left or right.
		That is, for this case we should distinguish C that have genus 1, from elliptic curves E that have a K-point (or, in other words, provide a Diophantine equation that has a solution in K).
		The term torsor is also used without the transitivity condition, especially in sheaf theory.
	en.wikipedia.org /wiki/Principal_homogeneous_space (931 words)

	Torsors
		To me, the interesting thing about the concept of a torsor is that it makes it clear that there's a mathematical justification for why addition and subtraction (or multiplication and division) might not have the same types.
		I think it's supposed to be the other way around, with documents being the torsor, and diffs just being a plain old group (assuming no such thing as rejected diffs).
		As far as I understood it, the whole torsor idea applies to plain old groups, and inverses are not needed.
	www.kimbly.com /blog/000445.html (770 words)

	[No title]
		Finally, if L is a torsor over G, let (L) be the torsor over G x G whose fibr* e at (g; h) is (L)g;hdef=Lg+h_L: g Lh A cubical structure on L is a particular sort of symmetric biextension structur *e on (L) [2, 2.2].
		A rigid torsor over G is a torsor L equipped with a section of the fibre L0 o* *ver the identity.
		G is a rigid torsor, then a rigid cubical structure on L is a cubical structure w* *hose various identity sections coincide with the sections produced from the rigid structure.
	hopf.math.purdue.edu /Ando-Strickland/pairings.txt (4802 words)

	The Galois action on the torsor of homotopy classes of paths on a projective line minus a finite number of points, by ... (Site not responding. Last check: 2007-10-15)
		The Galois action on the torsor of homotopy classes of paths on a projective line minus a finite number of points, by Zdzislaw Wojtkowiak
		We are studying the action of the Galois groups on torsors of paths on a projective line minus several points.
		In case of $\mathbb{P}^1 \setminus \{ 0, 1, \infty \}$ and a torsor of paths from $\vec 01$ to $-1$ we showed that the Lie algebra of derivations associated with the image of $Gal(\bar Q/Q_{\mu _{l^\infty }})$ is free on generators in degre e $1,3,5,\ldots 2n+1,\ldots $.
	www.math.uiuc.edu /K-theory/0606 (128 words)

	Amazon.com: "universal torsor": Key Phrase page (Site not responding. Last check: 2007-10-15)
		We first give precise criteria for when there exists a universal torsor for a large class of varieties over a number field k.
		One necessary condition is that there are universal torsors...
		Torsors and Rational Points (Cambridge Tracts in Mathematics) by Alexei Skorobogatov
	www.amazon.com /phrase/universal-torsor (408 words)

	Re: This Week's Finds in Mathematical Physics (Week 210)
		Its phase will change when > we do this, so we get two points in a U(1) torsor, and their difference > is an element of U(1).
		Then a > Anyway, the concept of relative phase, or difference in phase, is nicely > captured by the concept of a "torsor".
		A unit complex number is a point > on the unit circle in the complex plane.
	www.lns.cornell.edu /spr/2005-01/msg0066709.html (543 words)

	This Week's Finds in Mathematical Physics (Week 210)
		Anyway, the concept of relative phase, or difference in phase, is nicely captured by the concept of a "torsor".
		For more on torsors, try this: 3) John Baez, Torsors made easy, http://math.ucr.edu/home/baez/torsors.html Anyway, the real idea behind electromagnetism is that sitting over each point in spacetime is a U(1) torsor.
		Its phase will change when we do this, so we get two points in a U(1) torsor, and their difference is an element of U(1).
	www.lns.cornell.edu /spr/2005-01/msg0066695.html (3404 words)

	On a torsor of paths of an elliptic curve minus a point, by Zdzislaw Wojtkowiak (Site not responding. Last check: 2007-10-15)
		On a torsor of paths of an elliptic curve minus a point, by Zdzislaw Wojtkowiak
		We are studying some aspects of the action of the Galois groups on torsors of paths on an elliptic curve minus a point.
		We construct objects which behaviour is similar to the classical polylogarithms on the projective line minus three points.
	www.math.uiuc.edu /K-theory/0608 (71 words)

	Dimensional Analysis \| The n-Category Café
		But: if the torsor quantity is independent of units, and the torsor is dimensionless, then clearly the numerical quantity associated to the torsor is also independent of units.
		In particular, the multiplicative group R_+^3, which acts on the identifications between the mass torsors, length torsors, time torsors, and numbers (otherwise known as the unit mass, unit length, and unit time), then naturally acts on the identifications of all other torsors as well.
		One could of course choose other torsors to be the generators (provided they are a basis), and one would get a slightly different looking, but equivalent, notion of dimension.
	golem.ph.utexas.edu /category/2006/09/dimensional_analysis.html (10956 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		The argument is wrong because that classification of torsors only works for finite groups in the case of the algebraic fundamental groups (i.e., it is too good to be true).
		Moreover, one can construct counterexamples fairly easily: eg, take the trivial Z-torsor on P^1, glue the base to itself to get a nodal curve, and glue each component of the torsor to the next one.
		Max thinks he can prove that there are no Z-torsors on any X which is geometrically unibranch, so I think this says that one gets examples along the lines Jim had in mind for stacks of Z-torsors on the small etale site of a lot of schemes (but I guess this isn't nearly as interesting).
	math.stanford.edu /~vakil/727/jim (407 words)

	Amazon.com: "displacement torsor": Key Phrase page (Site not responding. Last check: 2007-10-15)
		1 Small displacement torsor A small displacement torsor is the formalization of a displacement for which a limited development to the first order of...
		The deviations of all the MMP surfaces are described with regards to their nominal position (nominal part) using a small displacement torsor.
		If the small displacement torsor is a useful tool to describe the relative situation of two simple surfaces, it's more difficult to describe the relative...
	www.amazon.com /phrase/displacement-torsor (576 words)

	Nabble - Positive integers (Site not responding. Last check: 2007-10-15)
		Surprisingly, there is a page on MathWorld about Torsors but it is
		Torsor is not quite the right word -- it's just that one of the contexts
		So "torsor" is just a short name for "regular group
	www.nabble.com /Positive-integers-t1333700.html (2725 words)

	TORSOR – Music at Last.fm (Site not responding. Last check: 2007-10-15)
		TORSOR isn’t yet available to play on Last.fm radio.
		TORSOR might not be making music anymore, but if they are, you can help keep other users informed by adding new events when they're announced.
		Music Journals on Last.fm You can be the first person to write a journal about TORSOR.
	www.last.fm /music/TORSOR (100 words)

	How many Circles are there in the World? \| The String Coffee Table
		Try to build a bundle of categories whose typical fiber is a torsor for that.
		-torsors and whose morphisms are torsor morphisms (HDA V, p.
		, the space of torsor morphisms between them is
	golem.ph.utexas.edu /string/archives/000867.html (915 words)

	This Week's Finds in Mathematical Physics (Week 210) Text - Physics Forums Library
		Weyl had a hint of it in 1918 when he invented\nthe term "gauge theory" in his quest to unify electromagnetism and gravity,\nbut he was mixed up in some crucial ways that only got sorted out quite\na bit later.
		Its phase will change when\nwe do this, so we get two points in a U(1) torsor, and their difference\nis an element of U(1).\n\nSo while it sounds far-out, the key mathematical structure in electromagnetism\nis a bunch of U(1) torsors, one over each point in spacetime.
		Its phase will change when\nandgt; we do this, so we get two points in a U(1) torsor, and their difference\nandgt; is an element of U(1).\nandgt;\nandgt; So while it sounds far-out, the key mathematical structure in electromagnetism\nandgt; is a bunch of U(1) torsors, one over each point in spacetime.
	www.physicsforums.com /archive/index.php/t-61495.html (5714 words)

	NAALive - HALF TORSOR MANEQUIN W/SUPER 110'S BUSINESS SUIT
		NAALive - HALF TORSOR MANEQUIN W/SUPER 110'S BUSINESS SUIT
		Proxy bids accepted until the lot is opened for live bidding (i.e.
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	www.naalive.com /cataloglistingitem.aspx?lotid=1415239 (82 words)

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