Bonn Topology Group - Abstracts

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Talk

November 10th 2020
Jim Davis (Indiana University, Bloomington, USA): Hyperfield Grassmannians

Abstract

The Grassmannian of k-planes in R^n is a classical object, useful in topology, geometry, and combinatorics. The cohomology of the Grassmannian gives all the characteristic classes of vector bundles. A hyperfield is a generalization of a field, but with multivalued addition. The main example for the talk will be the sign hyperfield S = {+,0,-}. Laura Anderson and I define the notion of a topological hyperfield and the Grassmannian of a hyperfield, and give a partial computation of the mod 2 cohomology of the Grassmannian of the sign hyperfield, showing that it contains the ring of Stiefel-Whitney classes. One of the tools organizing these ideas is the up-topology on a finite poset. This talk with give a survey of these topics and an indication of the many open questions surrounding them.

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