The collapse of the periodicity sequence in the stable range

2006/01/13 by Birgit Richter, Richter, Birgit
Computer Science · Mathematics · Physics and Astronomy · #13D03 #18G15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.math/0601326

openalex publication_date 2006/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The stabilization of Hochschild homology of commutative algebras is Gamma homology. We describe a cyclic variant of Gamma homology and prove that the associated analogue of Connes' periodicity sequence becomes almost trivial, because the cyclic version coincides with the ordinary version from homological degree two on. We offer an alternative explanation for this by proving that the B-operator followed by the stabilization map is trivial from degree one on.

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