2024/03/25 by Taniguchi, Toyo
#16E05 #16E10 #16S34 #16T05 #57K20 (primary) 16D20 #58B34 (secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2403.16566
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.