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arXiv · 2403.16566

Non-commutative divergence and the Turaev cobracket

Toyo Taniguchi
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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.

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Toyo Taniguchi. 2024-03-25. Non-commutative divergence and the Turaev cobracket. https://doi.org/10.2140/agt.2025.25.3103

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