# Questions tagged [homotopy-theory]

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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### Snaith splitting for operads in spectra?

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### Computing the differentials in the Adams spectral sequence

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### Cohomogy of local systems over CW-complexes

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### Italian-style algebraic geometry in homotopy theory?

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### Homotopy colimits of simplicial objects

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### What is the generator of $\pi_9(S^2)$?

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### Analog of cellular approximation theorem for $CW_0$-complexes ($CW_\mathcal P$-complexes)

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### homotopy VS isotopy classes of embeddings

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### Homotopy of rigid analytic spaces

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### A question about the group $[HZ,KU]$

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### Local quotient covers for derived Deligne-Mumford geometric stacks of Toen-Vezzosi

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### How weird can a ring spectrum be if all of its modules are free?

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### Examples and non-examples of Tannakian $\infty$-categories

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### A question about maps of spectra

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