Eight flavours of cyclic homology
K. Cieliebak (Universit\"at Augsburg), E. Volkov (Universit\"at Augsburg)
TL;DR
This paper introduces eight variants of cyclic homology for mixed complexes and explores their properties, especially their behavior under Chen iterated integrals, advancing understanding in algebraic topology and homological algebra.
Contribution
It systematically defines and analyzes eight different cyclic homology theories for mixed complexes, highlighting their properties and interactions with Chen integrals.
Findings
Eight new cyclic homology variants introduced
Detailed analysis of their properties and relations
Behavior under Chen iterated integrals elucidated
Abstract
We introduce eight versions of cyclic homology of a mixed complex and study their properties. In particular, we determine their behaviour with respect to Chen iterated integrals.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Axial and Atropisomeric Chirality Synthesis