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In this thesis we deal with questions of continuous group cohomology of continuous representations of a separable locally compact group on a real or complex Banach space. Of particular importance is the case of a compact group. Here we use a ne actions to prove vanishing theorems. To do this, we give an alternative de nition of the cohomology, which is recursive. As a consequence we prove under certain conditions (equivalent with the existence of a non-trivial simultaneous xed point of the associated a ne map) all cohomology groups vanish. When G is a connected Lie group, we study the relationship of its cohomology with the corresponding Lie algebra cohomology. Finally, we consider the situation of a closed subgroup H of G which is cocompact and of co nite volume and show just as in the case of a compact group that the restriction map H^n(G,V)--H^n(H,V) is injective and apply this to questions of complete reducibility of representations.
About the author
Ioannis Farmakis is an Assistant Professor in Mathematics. He received his PhD. from The Graduate Center (CUNY), New York, his M.A. from Hunter College (CUNY), and his B.A. from the University of Athens, Greece. His interests are on Lie Groups and their Representations, Algebra and Geometry. He teaches Mathematics at St. Francis College and at Brooklyn College (CUNY). He lives in Brooklyn, New York.
