Non-commutative divergence and the Turaev cobracket
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.
Cite
@article{arxiv.2403.16566,
title = {Non-commutative divergence and the Turaev cobracket},
author = {Toyo Taniguchi},
journal= {arXiv preprint arXiv:2403.16566},
year = {2025}
}
Comments
25 pages, Section 6 is massively re-organised. This is the version submitted to AGT with a slight correction of typos