Explicit Homotopy Equivalences Between Some Operads

Details Explicit Homotopy Equivalences Between Some Operads Explicit Homotopy Equivalences Between Some Operads

2011-10-14

arxiv.org/abs/1110.3116v1

Mathematics

Algebraic Topology

Scientific paper

In this work we present an explicit operad morphism that is also a homotopy equivalence between the operad given by the real Fulton MacPherson compactification of configuration spaces and the little $n$-disks operad. In particular, the construction gives an operadic homotopy equivalence between the associahedra and the little intervals explicitly. It can also be extended to the case of Kontsevich compactification and Voronov swiss-cheese operad.

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