All Questions
Tagged with kt.k-theory-and-homology spectral-sequences
8 questions with no upvoted or accepted answers
10
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325
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Adams blue book lemma 17.14: computing a $\mathbb{F}_2$ basis for a filtration of $H\mathbb{Z}_*(bu \wedge bu)$
First off let me apologize for not being able to give all the context for this question. I'm learning how to do computations in stable homotopy theory and have been particularly spending a lot of time ...
- 101
10
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352
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Is there a spectral sequence of Atiyah's topological KR-theory that can be used to compute basic examples?
For Segal's complex $G$-equivariant $K$-theory, it is well-known that there is an Atiyah-Hirzebruch spectral sequence. If say $G$ a finite group and $X$ a finite CW-complex, the second page of this ...
- 357
7
votes
0
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541
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Convergence of a spectral sequence of a double complex
In Weibel's book, a spectral sequence $E^r_{p,q}$ is said to weakly converge to a graded object $H_{\ast}$ if for every $n$ there exists a filtration $\dots \subset F_{r}H_{n} \subset F_{r-1}H_{\ast} \...
- 1,325
7
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0
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436
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spectral sequence for a complex with two filtrations
Suppose $(C,d)$ is a chain complex: an abelian group with a map $d:C \to C$ such that $d^2 = 0$ (people like to assume $C$ is graded; if that helps - feel free to do so). A filtration is an ascending ...
- 353
6
votes
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163
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Spectral Sequence for Twisted K-theory
Atiyah and Segal wrote in their Twisted K-theory that one can compute twisted K-theory using a spectral sequence similar to an Atiyah-Hirzebruch spectral sequence. They claimed that for any twisting $[...
- 61
5
votes
0
answers
521
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Spectral sequences coming from filtrations (Postnikov systems) in triangulated categories: references and convergence
Let $c^i: M^{\ge i+1}\to M^{\ge i}$ for $i\in \mathbb{Z}$ be an sequence of morphisms in a triangulated category $C$ and assume that $M^{\ge i}$ are equipped with compatible morphisms into an object $...
- 16.9k
3
votes
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122
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Twisted spin cobordism v.s. KO theory in low dimensions
Based on the background info and this this webpage, here is a more advanced problem:
Question: If we consider a different more subtle twisted structure, like
$${\Omega_d^{(\mathrm{spin} \times G)/N}},...
- 10.5k
0
votes
0
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80
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Relation between Chow groups and K theory
I am reading about Chow groups and algebraic K-theory of schemes. I get to know that for smooth schemes the re is a strongly convergent spectral sequence
$$E_2^{p,q} = CH^{-q}(X,-p-q) \implies K_{-p-q}...
- 613