Volume 19, issue 6 (2019)

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Coproducts in brane topology

Shun Wakatsuki

Algebraic & Geometric Topology 19 (2019) 2961–2988
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 1. The key to extending the loop coproduct is the fact that the embedding M MSk1 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