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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.

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