Australian Mathematical Society
Mathematics Department at Macquarie University

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50th Annual Meeting of the Australian Mathematical Society

Plenary Talk in Macquarie Theatre

Wednesday 27 September 2006 at 11:30


Michael Batanin (Macquarie University)


Configuration Spaces from Combinatorial, Topological and Categorical Perspectives


The topology of n-fold loop spaces has been studied extensively in the 1960s and 1970s. Yet, a full understanding of this topology has been reached only for n=1 in the works of Stasheff, who constructed a sequence of convex polytopes, later called associahedra, and showed that the loop space structure on a space is governed by the combinatorics of these polytopes. The analogues of associahedra for n>1 have remained mysterious for more than 40 years.

It was observed at the beginning of 1990s that the k-th associahedron can be obtained as Fulton-Macpherson compactification of moduli space of configurations of k distinct points on a real line. In my lecture I will show how to generalise this observation to produce the analogues of Stasheff's polytopes in all dimensions using ideas from higher category theory.