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Results tagged with homotopy-theory
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user 141953
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.
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Trivial homology with local system
Let $X$ be the classifying space of the Higman group $G$. It is well known that $G$ is an acyclic group
$$H_{\ast}(X;\mathbb{Z})=H_{\ast}(pt;\mathbb{Z}).$$
Now, suppose that $\mathcal{M}$ is a loca …
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