Smooth deformations and the Gauss-Manin connection

2014/10/02 by Allan Yashinski, Yashinski, Allan
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1410.0715

openalex publication_date 2014/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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