String Topology for Embedding Spaces

Abstract

We extend the structure of string topology from mapping spaces to embedding spaces $Emb(S^n,M)$. This extension comes from an action of the cleavage operad, a coloured $E_{n+1}$-operad. For all values of $n\in \mathbb{N}$, this gives an action of certain Thom spectra that provides an action on the level homology. We provide an analysis of the string topology structure derived from the embedding $Emb(S^n,M)\hookrightarrow Map(S^n,M)$. In the $1$-dimensional case it specializes a morphism of BV-algebras ${\mathbb{H}}_{\ast }(Emb(S^1,M))\to {\mathbb{H}}_{\ast }(Map(S^1,M)$.

References in corpus (1)

• Higher string topology operations