The Combinatorics of Iterated Loop Spaces

Michael Batanin

    Research output: Contribution to conferenceAbstract


    It is well known since Stasheff's work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads. The combinatorics of these higher homotopies is well understood and is extremely useful. For $n ge 2$ the theory of symmetric operads encapsulated the corresponding higher homotopies, yet hid the combinatorics and it has remain a mystery for almost 40 years. However, the recent developments in many fields ranging from algebraic topology and algebraic geometry to mathematical physics and category theory show that this combinatorics in higher dimensions will be even more important than the one dimensional case. In this paper we are going to show that there exists a conceptual way to make these combinatorics explicit using the so called higher nonsymmetric $n$-operads.
    Original languageEnglish
    Number of pages1
    Publication statusPublished - 2003
    EventFifth International Conference on Industrial and Applied Mathematics - Sydney, Australia
    Duration: 7 Jul 200311 Jul 2003


    ConferenceFifth International Conference on Industrial and Applied Mathematics
    CitySydney, Australia

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