Explicit Homotopy Equivalences Between Some Operads

2011/10/14 by Eduardo Hoefel, Hoefel, Eduardo
Biochemistry, Genetics and Molecular Biology · Mathematics · #55P10 #55P48 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.1110.3116

openalex publication_date 2011/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Operads, configuration spaces and quantization

Related

• Little discs operads, graph complexes and Grothendieck--Teichmüller groups
• Homotopy derivations of the framed little discs operads
• Formality of the little N-disks operad
• The Swiss-Cheese Operad
• A Compactification of the Real Configuration Space as an Operadic Completion