Algebra and Topology Seminar

4pm Tuesday 19 October 2004
Michael Batanin
Macquarie University

Coherence for higher homotopy commutativity

The combinatorics of coherence laws for higher homotopy associativity is well understood since Stasheff's works. They are given by a sequence of polytopes known as associahedra which are nicely organised in a nonsymmetric operad.

In contrast the study of this combinatorics when commutativity is involved has remained a sort of mysterious art for almost 40 years.

In my talk I will explain how we can approach this problem systematically using the theory of higher nonsymmetric operads. I will also explain how we can organise the higher coherence laws and how they interact to each other in an unexpected manner.




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