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Results tagged with homotopy-theory
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user 5010
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.
51
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3
answers
12k
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Spaces with same homotopy and homology groups that are not homotopy equivalent?
A common caution about Whitehead's theorem is that you need the map between the spaces; it's easy to give examples of spaces with isomorphic homotopy groups that are not homotopy equivalent. (See Are …
- 10.1k
4
votes
Accepted
Unordered configuration space of $\mathbb{R}P^1$
(1) and (2) are perfectly compatible, to the extent which (1) makes sense. $\mathbb{R}P^k$ is naturally a CW complex with one cell in each dimension, and $\mathbb{R}P^{k-2}$ is a subcomplex. Assuming …
- 10.1k
6
votes
Accepted
unordered configuration space of pointed space
With your definitions, assuming you mean the configuration space of distinct points, and that the inclusions need to be compatible with the actual locations of the points in some way, there is not suc …
- 10.1k