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Results tagged with homotopy-theory
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user 31233
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.
6
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Grothendieck spectral sequence and Mayer-Vietoris sequence
Here is a slightly different argument than algori's, not using the construction of the Čech-to-derived functor spectral sequence and only using $E_2$ terms, not $E_1$ terms.
As you say, the spectral …
- 3,312
6
votes
1
answer
377
views
Elementary proof of the exactness of Čech complex associated to a hypercovering ("Illusie's ...
Let $\mathcal{E}$ be a sheaf of abelian groups on a topological space (or a site). For an open covering $\mathfrak{U} = (U_i)_i$, it is well known that the augmented Čech complex $0 \to \mathcal{E} \t …
- 3,312