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arXiv · 2510.05997

String topology coproduct and Turaev cobracket on surfaces

Jana Hartenstein·Maximilian Stegemeyer
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Abstract

The string topology coproduct on the homology of the free loop space of a closed manifold induces a string cobracket on $S^1$-equivariant homology. We give a complete computation of the string topology coproduct for surfaces of higher genus by describing an algorithm which computes the coproduct of a cyclic word in terms of generators of the fundamental group of the surface. We further show that the string cobracket is the negative of the Turaev cobracket.

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Jana Hartenstein, Maximilian Stegemeyer. 2025-10-07. String topology coproduct and Turaev cobracket on surfaces. https://arxiv.org/abs/2510.05997

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