Steenrod operations via higher Bruhat orders

Abstract: The cohomology of a topological space has a ring structure via the cup product. The cup product is defined at the level of cochains, where it is not commutative, but it becomes commutative at the cohomology level. At the cochain level, the lack of commutativity is resolved homotopically by an infinite tower of higher products, known as the Steenrod cup-i products. This additional structure provides more refined information which can be used to tell apart non-homotopy-equivalent spaces. Not assuming any background from algebraic topology, I will explain recent work with Guillaume Laplante-Anfossi, where we show how conceptual proofs of the key properties of Steenrod's cup-i products can be given using the higher Bruhat orders of Manin and Schechtman.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.