# Questions tagged [k-homology]

The k-homology tag has no usage guidance.

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### 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 ...

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### 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 ...

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### 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 ...

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### 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**

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### 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. ...

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### 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 ...