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Results tagged with homotopy-theory
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user 3969
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.
5
votes
1
answer
296
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Massey Products on a specific space
Let $a,b$ be the canonical generators of $\pi_1(S^1\vee S^1)$ corresponding to the edges with some choice of orientation.
Are there nonzero-Massey products in the cohomology with $\mathbb{F}_2$-coeff …
- 11.1k
8
votes
Accepted
homotopy associative $H$-space and $coH$-space
I looked at my homotopy theory lecture notes and we had the following similar result:
$X$ H-CoGroup, $Y$ $H$-Group, then both group structures defined on [X,Y] agree.
The proof goes roughly as follows …
- 11.1k
6
votes
Accepted
Massey Products on a specific space
Here a general way how to compute Massey Products on nice spaces.
The first step would be to realize the space as the geometric realization of a simplicial set. I used the simplicial set given by the …
- 11.1k
4
votes
What is known about this cohomology operation?
Here are some examples. And since this really just adresses the computation part of the question and not what that map is, it is really just a partial answer.
LEt me first describe the sequence oper …
- 11.1k
2
votes
0
answers
108
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DGAs with pointwise Multiplication
The singular cochain complex of a space can be equipped with another product, the pointwise product of two cochains
\[\odot: C^n \otimes C^n\rightarrow C^n \qquad \Psi_1 \odot \Psi_2 (f:\Delta^n\righ …
- 11.1k