On the Cohomology of Topological Semigroups

Year 2019, Volume: 2 Issue: 3, 206 - 212, 30.09.2019

Maysam Maysami Sadr Danial Bouzarjomehri Amnieh

https://doi.org/10.33434/cams.515711

Abstract

In this short note, we give some new results on continuous bounded cohomology groups of topological semigroups with values in complex field. We show that the second continuous bounded cohomology group of a compact metrizable semigroup, is a Banach space. Also, we study cohomology groups of amenable topological semigroups, and we show that cohomology groups of rank greater than one of a compact left or right amenable semigroup, are trivial. Also, we give some examples and applications about topological lattices.

Keywords

Topological semigroup, bounded cohomology, Banach homology

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