IJPAM: Volume 58, No. 3 (2010)

AN ALTERNATIVE DEFINITION OF CONTINUOUS
COHOMOLOGY AND A VANISHING THEOREM

Ioannis Farmakis
The Doctorate-Graduating Institution
The City University of New York (CUNY)
365, Fifth Ave., New York, NY 10016, USA
e-mail: [email protected]


Abstract.Given a locally compact group $G$ and a continuous representation $\rho$ of $G$ on a real or complex Banach space $V$ we obtain the corresponding cohomology groups $H^{n}(G,V,\rho)$ using a recursive construction adapted from [1]. As a consequence we prove under certain conditions (equivalent with the existence of a non-trivial simultaneous fixed point of the associated affine map) that all cohomology groups vanish.

Received: December 10, 2009

AMS Subject Classification: 22D12, 22E41, 57T10

Key Words and Phrases: continuous cohomology of groups and its vanishing, continuous representation, affine map, fixed point, short and long exact sequence, $n$-cochain, $n$-coboundary

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 3