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.
- Finite-dimensional representations
- automatic closure
- reduced cohomology
ASJC Scopus subject areas
- Geometry and Topology