Talk:Twisted K-theory

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[edit] Category

Really you think that this page should be listed in the "Mathematics" category? I would have thought that it's too specific (that is, it exists inside of many subfields, but it isn't itself a subfield, after all ordinary K-theory isn't listed on Mathematics) and should just be in Topology, in K-Theory, maybe in Geometry or String Theory ... JarahE

No it shouldn't, I removed it. Person who added the cat probably didn't understand math well enough to figure out the correct subcats. linas 02:10, 14 March 2006 (UTC)

[edit] Projective unitary operator

Can you add a definition of a "projective unitary operator" to the article Unitary operator? I'm having trouble guessing what this is. I keep thinking that maybe its related to the Classifying space for U(n) but I can't quite wrap my mind around it. linas 02:10, 14 March 2006 (UTC)

I'll take a look. The classifying space is BU(H). The projective unitary operators, PU(H), are different (even topologically, PU(H) is a K(Z,2), BU(H) satisfies a mod 2 Bott periodicity). PU(H) is the quotient of U(H) by its center, which is U(1). It's the infinite-dimensional analogue of PU(N), which is the quotient of U(N) by its center U(1), for example PU(2)=SO(3) JarahE 18:36, 14 March 2006 (UTC)

Ahh, OK. Somehow my mind froze when I saw that. linas 00:56, 15 March 2006 (UTC)

[edit] Atiyah's result

The article refers to "Atiyah's result", I presume this is the Atiyah–Singer index theorem? If so, that artcile should be linked. linas 02:14, 14 March 2006 (UTC)

No, it's not the index theorem. Embarassingly, I don't know where Atiyah published it. I found it in the paper Twisted K-theory and the K-theory of Bundle Gerbes, which I've been meaning to add to this article anyway as bundle gerbes are useful to construct characteristic classes for twisted K-theory. But the authors just refer to it as Atiyah's result, I guess it must be so well known that they don't feel the need to reference it. But I would like to know where Atiyah published this. JarahE 18:36, 14 March 2006 (UTC)