Coproducts in brane topology

Wakatsuki, Shun

doi:10.2140/agt.2019.19.2961

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Coproducts in brane topology

Shun Wakatsuki

Algebraic & Geometric Topology 19 (2019) 2961–2988

DOI: 10.2140/agt.2019.19.2961

Abstract

We extend the loop product and the loop coproduct to the mapping space from the $k$ –dimensional sphere, or more generally from any $k$ –manifold, to a $k$ –connected space with finite-dimensional rational homotopy group for $k \geq 1$ . The key to extending the loop coproduct is the fact that the embedding $M \to M^{S^{k - 1}}$ is of “finite codimension” in the sense of Gorenstein spaces. Moreover, we prove the associativity, commutativity and Frobenius compatibility of them.

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Keywords

string topology, brane topology, Gorenstein space, rational homotopy theory

Mathematical Subject Classification 2010

Primary: 55P35, 55P50, 55P62

References

Publication

Received: 29 March 2018

Revised: 17 December 2018

Accepted: 31 January 2019

Published: 20 October 2019

Authors

Shun Wakatsuki
Graduate School of Mathematical Sciences The University of Tokyo Tokyo Japan

Volume 19, issue 6 (2019)