Approximate cohomology in Banach algebras
Ahmad Shirinkalam, A. Pourabbas
TL;DR
This paper introduces the concepts of approximate cohomology and homotopy in Banach algebras, exploring their relationships and special cases like approximate Hochschild cohomology.
Contribution
It defines approximate cohomology and homotopy in Banach algebras and analyzes their interrelations, including the case of Hochschild cohomology.
Findings
Approximate homotopically equivalent complexes have identical approximate cohomologies.
Approximate Hochschild cohomology is introduced and studied as a special case.
Abstract
We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As an special case, approximate Hochschild cohomology is introduced and studied.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra