Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with kt.k-theory-and-homology
Search options answers only
not deleted
user 402
Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
51
votes
Accepted
What are surprising examples of Model Categories?
Here is an example that surprised me at some time in the past.
Bisson and Tsemo introduce a nontrivial model structure on the topos of directed graphs.
Here a directed graph is simply a $4$-tuple $(V, …
- 37.8k
12
votes
What is decategorification?
Taking loops (or, in categorical language, endomorphisms of the monoidal unit) is commonly seen as a type of decategorification.
For example, decategorifying von Neumann algebras produces Hilbert spac …
- 37.8k
7
votes
Invertibility of element in $K(X)$
Yes. Any rank zero element x in K(X) is nilpotent by https://ncatlab.org/nlab/show/virtual%20vector%20bundle, hence 1+x is invertible.
- 37.8k
6
votes
Accepted
Can one bypass the geometric realization in the definition of algebraic $K$-theory?
I believe there is no good notion of homotopy groups for an arbitrary simplicial set S.
It depends on what “good” means.
Kan's original definition works for arbitrary pointed simplicial sets: $$\def …
- 37.8k
4
votes
K-theory of non-compact spaces
What exactly does 3. describe? Are these virtual vector bundles that admit numerable trivializations?
Virtual vector bundles, when defined as formal differences (i.e.,
elements in the homotopy gr …
- 37.8k
3
votes
Accepted
Reference for $E_{\infty}$-ness of the Chern Character
The answer really depends on one's desired choice of definitions for KU, HQ, and the Chern character itself;
some definitions allow one to produce a very short definition of the Chern character as an …
- 37.8k
1
vote
A question on the ring structure of topological K-theory and Chern character
The product of $K^{−1}$ with itself can be defined by identifying $K^{−1}(X)$
with $K^0(X\wedge S^1)$ using the suspension isomorphism, multiplying the resulting two elements of $K^0(X\wedge S^1)$, o …
- 37.8k