Configuration
Spaces from Combinatorial, Topological andCategorical 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.
