Cyclic diagonals of the associahedra

Thursday, January 23, 2014 - 3:30pm
MSB 111
Junwu Tu (University of Oregon)

In the 1960s, Jim Stasheff, in order to formulate a homotopy coherent associativity structure underlying based loop spaces, discovered a fundamental object of mathematics: the associahedra. These are convex polytopes in Euclidean spaces which neatly organize higher associativity by their facets. In this talk, we first review Stasheff¹s construction, assuming a little acquaintance of the fundamental group of a topological space. Then we shall prove that the linearized associahedra admit a cyclically invariant diagonal which is unique up to homotopy. This leads to interesting applications, both in algebra and in topology.

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