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Results tagged with kt.k-theory-and-homology
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user 5792
Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
8
votes
1
answer
297
views
Equivariant bundles invisible in K-theory and Borel cohomology
For a given topological group $G$ there are natural transformations $$K^* \leftarrow K^*_G \overset a\to H^{**}(EG \times_G -;\mathbb Q)$$ from equivariant K-theory, the first forgetting the $G$-struc …
- 2,995
20
votes
1
answer
1k
views
Torsion in the Atiyah–Hirzebruch spectral sequence of a classifying space
Let $G$ be a compact, connected Lie group. There is an Atiyah–Hirzebruch spectral sequence
$$H^*(BG;K^*) \implies K^*(BG)$$
connecting $H^*BG$, which generally contains torsion, with $K^*BG \cong \ …
- 2,995
9
votes
Is there any "deep" relation between the localization theorem of equivariant cohomology and ...
This is very late and you've no doubt learned this in the last five years, but for completeness, the relation is indeed that they are linked by completion and the Chern character, as suggested in one …
- 2,995
48
votes
0
answers
17k
views
What is the current understanding regarding complex structures on the 6-sphere?
In October 2016, Atiyah famously posted a preprint to the arXiv, "The Non-Existent Complex 6-Sphere" containing a very brief proof $S^6$ admits no complex structure, which I immediately read and reali …
- 2,995
6
votes
What is the equivariant cohomology of a group acting on itself by conjugation?
For any interested latecomers who somehow discover this question in the future, I've found a very low-tech answer, bootstrapping from the low-tech answer to Is a Lie group equivariantly formal under c …
- 2,995