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.

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)