CRM: Centro De Giorgi
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Combinatorics and Algebraic Topology of Configurations

Some intersections of quadrics arising from division algebras "Combinatorics and Algebraic Topology of Configurations" (Workshop 2015)

speaker: Matthias Franz (University of Western Ontario)

abstract: I will present a small family of intersections of quadrics involving the normed real division algebras. These spaces are smooth manifolds and come with a canonical action of the $2$-torus $G=\{\pm1\}n$. They turn out to be equivariantly homeomorphic to the real version of the ``mutants of compactified representations'' introduced by Franz and Puppe, which implies that their equivariant cohomology has interesting features. Moreover, these quadrics can be realized as intersections of products of spheres with linear subspaces, and they are diffeomorphic to connected sums of products of spheres. If time permits, I will discuss some generalizations of the construction.

Wed 18 Feb, 10:40 - 11:20, Aula Dini
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