Michael Batanin
Macquarie University, Sydney, Australia

Recognition of n-Fold Loop Spaces and n-Categories

n-Fold loop spaces play a central role in algebraic topology. A
classical problem is to describe algebraic structure on a space which
makes it equivalent to an n-fold loop space in terms of a set of
operations and relations between them. This is so called coherence
problem for n-fold loop spaces. In 1963 Stasheff fully answered this
question for n=1 using a beautiful sequence of polyhedra which was
later called associahedra.

In my lecture I will show how one can generalize Stasheff's theory for
arbitrary n using ideas which came from n-category theory. I will try
to make my exposition informal and comprehensible. No prior knowledge
of n-category theory is required.