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Mathematics > Algebraic Topology
Title: Non-commutative divergence and the Turaev cobracket
(Submitted on 25 Mar 2024 (v1), last revised 4 May 2024 (this version, v3))
Abstract: The divergence map, an important ingredient in the algebraic description of the Turaev cobracket on a connected oriented compact surface with boundary, is reformulated in the context of non-commutative geometry using a flat connection on the space of 1-forms on a formally smooth associative algebra. We then extend this construction to the case of associative algebras with any finite cohomological dimension, which allows us to give a similar algebraic description of the Turaev cobracket on a closed surface. We also look into a relation between the Satoh trace and the divergence map on a free Lie algebra via geometry over Lie operad.
Submission history
From: Toyo Taniguchi [view email][v1] Mon, 25 Mar 2024 09:33:01 GMT (26kb)
[v2] Tue, 26 Mar 2024 14:00:01 GMT (438kb)
[v3] Sat, 4 May 2024 04:34:43 GMT (21kb)
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