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Results tagged with homotopy-theory
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user 123432
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
10
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1
answer
357
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Example of non-transitive homotopy relation
$\DeclareMathOperator{\Hom}{Hom}$
Dear all,
The question is for teaching purposes and rather basic, so I hope that it also allows (relatively) easy answer.
By abstract homotopy theory we know that if …
- 1,759
7
votes
1
answer
390
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Thom spectrum in the definition of power operations
I am reading now Tyler Lawson's $E_n$ ring spectra and Dyer-Lashof operations form the Handbook of Homotopy Theory and I've got a question on the Remark 1.4.19.
We have an operad $\mathcal{O}$ and $\ …
- 1,759
3
votes
2
answers
654
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Homology of a loop-suspension space and action of $\mathcal{D}_1$-operad
If $X$ is a based connected topological space, it is well-known what the homology of $\Omega\Sigma X$ is: according to the Bott-Samelson theorem, it is a tensor algebra over reduced homology of $X$. ( …
- 1,759
5
votes
1
answer
199
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May-McClure "A reduction of Segal conjecture"
I am looking for a digitalized version of paper by J.P. May and J. McClure A reduction of Segal conjecture, as I need it to understand some lemma from Kuhn's Tate Cohomology and Periodic Localization …
- 1,759
1
vote
0
answers
241
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A $d_1$-differential in the homotopy fixed points spectral sequence
I have the following problem. Let $Q$ denote $\mathbb{Z}/2$ as an abelian group and let $X$ be a $Q$-spectrum. If I want to compute the homotopy groups of $X^{hQ}$, homotopy fixed points spectrum, I c …
- 1,759
5
votes
0
answers
299
views
Relation between Bott-Samelson theorem and James reduced product
I asked this question on the homotopy theory chat, but I haven't got any answer - thus I decided to post it as a question here.
The question is rather historical. Let $X$ be a connected topological sp …
- 1,759
5
votes
2
answers
314
views
Reedy fibrancy and composition in Segal spaces
I am going through V. Hinich's "Lectures on Infinity Categories" and I have a (possibly trivial) question on Segal spaces.
We define Segal space to be a bisimplicial set $X$ which is fibrant in Reedy …
- 1,759
2
votes
1
answer
104
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DK equivalences are Reedy equivalences for complete Segal spaces
$\require{AMScd}$
Dear all,
I have a question concerning Charles Rezk's paper "A model for the homotopy theory of homotopy theory
", precisely Proposition 7.6 in this paper. It is proven there that if …
- 1,759