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Questions tagged [k-homology]

The tag has no usage guidance.

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0answers
389 views

Higher traces in Hochschild cohomology

Let $A$ be an associative algebra over a field $k$. Let $\rho:A \rightarrow \mathrm{End}(M)$ a left module, finite dimensional over $k$. Then the map $a \mapsto \mathrm{tr}_M \rho(a)$ is a well ...
2
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0answers
49 views

Understanding the relationship between Spin$^c$ orientations and Spin$^c$ structures

I'm looking for some guidance in understanding and writing down a proof of the following statement, concerning the relationship between Spin$^c$ structures and Spin$^c$ orientations, from an ...
4
votes
2answers
193 views

Differential structures and K-homology groups

What is an example of a (compact) manifold, which has two non-equivalent differential structures such that the K-homology groups are non-isomorphic? If no such example exists, i.e. "K-homology does ...
3
votes
1answer
367 views

K-homology of Cantor set and abelian AF-algebras

This may be a standard question answered in a book, or article. I don't know. I know that there exist related results with $\lim^1$-sequences (Rosenberg and Schochet). What is $KK(C_0(X),\mathbb{C})$...
4
votes
2answers
1k views

Lists of K-homology Groups

There sohould be a list of K-theory and K-homology groups for the the standard spaces, like circle, spheres, (non-commutative) tori, but despite I've googled for it, I have found nothing satisfying. ...
14
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0answers
667 views

Can we define spectral triples using the language of rigged Hilbert spaces?

The traditional mathematical approach to quantum mechanics, as developed by von Neumann, is based on Hilbert spaces and unbounded self-adjoint operators. Another approach, which more closely resembles ...