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Results tagged with kt.k-theory-and-homology
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user 5690
Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
9
votes
Mayer-Vietoris sequence for topological K-theory
"since $U_\pm$ are non-compact so I believe $K_0(U_\pm)$ should be the reduced $K_0$ of a 1-point compactification"
This is a convention often used in $K$-theory of $C^*$-algebras: by default, people …
- 43.2k
1
vote
K-theory space of a C*-algebra
The fundamental observation is that $\pi_1$ of the $E_\infty$-space $Pr(A\otimes \mathcal K)$ is stably abelian.
(Here "stably abelian" means that for any connected component $Y\subset Pr(A\otimes \m …
- 43.2k
5
votes
Homology or cohomology?
I would say that a cohomological chain complex has cohomology, and that a homological chain complex has homology...
- 43.2k
47
votes
Accepted
What are the "correct" conventions for defining Clifford algebras?
This is not really an answer, but rather a meta-answer as to why there exist many conventions in the first place.
The symmetric monoidal category $\mathit{sVect}$ of super-vector spaces has a non-tri …
- 43.2k
9
votes
Accepted
What is the "quaternionic" super Brauer group?
The Brauer-Picard 2-category of $SuperVect_{\mathbb R}$ (let's call it $sBrPic_\mathbb R$) is the homotopy fixed points of the Brauer-Picard 2-category of $SuperVect_{\mathbb C}$ w.r.t. the involution …
- 43.2k