Cosimplicial spaces and cocycles

J. F. Jardine

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arXiv · 1906.06274

Cosimplicial spaces and cocycles

J. F. Jardine

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Abstract

Standard results from non-abelian cohomology theory specialize to a theory of torsors and stacks for cosimplicial groupoids. The space of global sections of the stack completion of a cosimplicial groupoid $G$ is weakly equivalent to the Bousfield-Kan total complex of $BG$ for all cosimplicial groupoids $G$. The $k$-invariants for the Postnikov tower of a cosimplicial space $X$ are naturally elements of stack cohomology for the stack associated to the fundamental groupoid $\pi(X)$ of $X$. Cocycle-theoretic ideas and techniques are used throughout the paper.

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BibTeX RIS

J. F. Jardine. 2019-06-14. Cosimplicial spaces and cocycles. https://arxiv.org/abs/1906.06274

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