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KV-Cohomology and Differential Geometry of Affinely Flat Manifolds

Volume 14, Number 2 (2012), 197 - 226

KV-Cohomology and Differential Geometry of Affinely Flat Manifolds

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Abstract

This paper is devoted to the so-called twisted cohomology of Koszul-Vinberg algebras. We discuss relationships between the twisted cohomology of Koszul-Vinberg algebras and Chevalley-Eilenberg cohomology of the commutator algebra of these algebras. We also discuss some geometry applications of these relationships. For instance we obtain some homological criteria for hyberbolicity and for completeness of locally flat manifolds. We also discuss some topics which are related to twisted cohomology. In particular, we use some techniques of information geometry to discuss canonical representations of locally flat connections.