All Questions
8 questions
13
votes
1
answer
2k
views
Roadmap for Algebraic Geometry/Homotopy Theory/Algebraic $K$-Theory intersection
I’m afraid that this is quite a general question but I am hoping some experts can weigh in. I am a student generally interested in learning more about the intersection of algebraic geometry, algebraic ...
- 30.3k
1
vote
0
answers
104
views
Higher equivariance
The Atiyah-Segal completion theorem states that $K(BG) = \mathrm{Rep}(G) = K_G(*)$, when the left hand side is completed with respect to the augmentation ideal. In some sense, $G$-equivariant $K$-...
- 63.9k
3
votes
0
answers
180
views
$k$-invariants of $KO$ and $ko$ and differentials in the AHSS spectral sequence
Let $KO$ and $ko$ denote real $K$-theory and connective real $K$-theory. It appears to be a well done result that the $k$-invariants can be used to determine the early differentials in the Atiyah-...
- 855
7
votes
1
answer
448
views
Reference request for K-Theory linearization
I posted this question on math.se here:https://math.stackexchange.com/q/2996787/482732, but I think it may be more appropriate here, sorry if I am wrong about that.
In Waldhausen's paper Algebraic K ...
- 16.5k
9
votes
0
answers
371
views
Which of the physics dualities are closest in essence to the Spanier-Whitehead duality (with a subquestion)?
First of all, what I want to ask is slightly more elaborate than what stands in the title (hence the subquestion).
I am telling this since as it is, the title contains a meaningful question, but it ...
- 18.4k
4
votes
1
answer
166
views
On closed model categories: standard arguments and fibrantly cogenerated categories
Some not very clever questions on closed model categories.
For a (left or right) Quillen functor $F:C\to D$ what arguments does one usually use for proving that $Ho F$ is fully faithful when ...
- 651
4
votes
1
answer
204
views
Yoneda embeddings of stable model categories; composition with Bousfield localizations
For a stable model category $C$ and a set $M$ of object of it I would like to construct a natural functor from $C$ to some stable 'category of functors' on $M$. I suspect that the 'natural' question ...
- 15.2k
16
votes
2
answers
1k
views
Proof of Bott Periodicity in twisted K-theory
I have a question about the Proof of Bott Periodicity in twisted K-theory
by Atiyah and Segal in their paper Twisted K-theory.
Following their notation, to prove Bott periodicity in this context it ...
- 111