Smooth deformations and the Gauss-Manin connection
classification
🧮 math.KT
math.OA
keywords
algebrasconnectiongauss-maninsmoothcohomologycyclicperiodicassociative
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Given a smooth one parameter deformation of associative topological algebras, we define Getzler's Gauss-Manin connection on both the periodic cyclic homology and cohomology of the corresponding smooth field of algebras and investigate some basic properties. We use the Gauss-Manin connection to prove a rigidity result for periodic cyclic cohomology of Banach algebras with finite weak bidimension.
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