Stefan Schwede: University of Bonn : Mathematics Colloquium

Mathematics Colloquium II.

Speaker: Stefan Schwede.

Affiliation: University of Bonn.

Date and Time: Thursday 20 February, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Equivariant properties of symmetric products.

Abstract: The ultimate aim of this talk is to explain a calculation of
equivariant homotopy groups of symmetric products of spheres. To lead up
to this, I will review the notion of degree of a map between spheres, and
of its equivariant refinement, for a finite group G of equivariance. The
answer is best organized as an isomorphism, due to Graeme Segal, to the
Burnside ring of the finite group G.

The filtration of the infinite symmetric product of spheres by number of
factors has received a lot of attention in algebraic topology. We
investigate this filtration for spheres of linear representations of the
finite group G; by Segal's theorem, the resulting sequence of 0th
equivariant homotopy groups starts with the Burnside ring, and it ends in
a single copy of the integers (independent of the group of equivariance).
We describe this sequence in a uniform and purely algebraic manner,
including the effect of restrictions and transfers maps that connect the
values for varying groups G.

An effort will be made to make a good portion of the talk accessible to
graduate students.
Ramanujan Hall, Department of Mathematics
Thu, February 20, 2020
Start Time
4:00pm-5:00pm IST
1 hour
Created by
Mon, February 17, 2020 7:13am IST