The Cleavage Operad and String Topology of Higher Dimension

Details The Cleavage Operad and String Topology of Higher Dimension The Cleavage Operad and String Topology of Higher Dimension

2010-12-21

arxiv.org/abs/1012.4839v3

Mathematics

Geometric Topology

35 pages, 7 figures

Scientific paper

For a manifold N embedded inside euclidean space R^{n+1}, we produce a coloured operad that acts on the space of maps from N to M, where M is a compact, oriented, smooth manifold. For N the unit sphere, we indicate how this gives homological actions, generalizing the action of the Cacti operad and retrieving the Chas-Sullivan product by taking N to be the unit-circle in R^2. We go on to show that for S^n the unit sphere in R^{n+1}, the operad constructed is a coloured E_{n+1}-operad. This E_{n+1}-structure is finally twisted by SO(n+1) to homologically give (n+1)-Batalin-Vilkovisky Structures.

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