Euclidean-valued group cohomology is always reduced

Tim Austin

doi:10.1142/S1793525318500243

Euclidean-valued group cohomology is always reduced

Tim Austin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let K be a topological field and G a countable discrete group. Then for any linear G-Action on a finite-dimensional vector space over K, the groups of coboundaries in the inhomogeneous bar resolution are closed in all degrees, and hence the cohomology is reduced in all degrees. This can be deduced from a more general automatic-closure theorem for continuous linear transformations between inverse limits of finite-dimensional vector spaces.

Original language	English (US)
Pages (from-to)	483-491
Number of pages	9
Journal	Journal of Topology and Analysis
Volume	10
Issue number	3
DOIs	https://doi.org/10.1142/S1793525318500243
State	Published - Sep 1 2018

Keywords

Finite-dimensional representations
automatic closure
reduced cohomology

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1142/S1793525318500243

Cite this

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abstract = "Let K be a topological field and G a countable discrete group. Then for any linear G-Action on a finite-dimensional vector space over K, the groups of coboundaries in the inhomogeneous bar resolution are closed in all degrees, and hence the cohomology is reduced in all degrees. This can be deduced from a more general automatic-closure theorem for continuous linear transformations between inverse limits of finite-dimensional vector spaces.",

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AB - Let K be a topological field and G a countable discrete group. Then for any linear G-Action on a finite-dimensional vector space over K, the groups of coboundaries in the inhomogeneous bar resolution are closed in all degrees, and hence the cohomology is reduced in all degrees. This can be deduced from a more general automatic-closure theorem for continuous linear transformations between inverse limits of finite-dimensional vector spaces.

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KW - reduced cohomology

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Euclidean-valued group cohomology is always reduced

Abstract

Keywords

ASJC Scopus subject areas

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