#### 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 $k\ge 1$. 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