The Combinatorics of Iterated Loop Spaces

@inproceedings{BataninTheCO,
  title={The Combinatorics of Iterated Loop Spaces},
  author={Michael Batanin}
}
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 ≥ 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… CONTINUE READING
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