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Second cohomotopy and nonabelian cohomology

Published online by Cambridge University Press:  17 January 2014

Mariam Pirashvili
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Abstract

The main difficulty in the theory of non-abelian cohomology is that for cosimplicial groups only zero-th and first dimensional cohomotopy are known. In this article we introduce a new class of cosimplicial groups, called centralised cosimplicial groups, for which we are able to define a second cohomotopy, with all expected properties. The main examples of such cosimplicial groups come from 2-categories.

Keywords

Non-abelian cohomologycosimplicial groupstwisting by a cocycle18G5055U10
Type
Research Article
Information
Journal of K-Theory , Volume 13 , Issue 3 , June 2014 , pp. 397 - 445
Copyright
Copyright © ISOPP 2014 

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