Topology Seminar
Upcoming Talks
The seminar will meet at 4:30pm on Mondays in 2-131 unless otherwise noted.
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Roman Mikhailov (Steklov, Moscow, and IAS)
A combinatorial description of homotopy groups of spheres
The talk is based on recent results obtained jointly with Jie Wu. For all n > k, we construct a finitely generated group by explicit generators and relations such that its center is the n-th homotopy group of the k-th sphere.
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Stefan Schwede (Bonn)
Equivariant properties of symmetric products
Please note this will be a Tuesday talk. Usual time and room.
The filtration on the infinite symmetric product of spheres by number of factors provides a sequence of spectra between the sphere spectrum and the integral Eilenberg-Mac Lane spectrum. This filtration has received a lot of attention and the subquotients are interesting stable homotopy types. In this talk I will discuss the equivariant stable homotopy types, for finite groups, obtained from this filtration for the infinite symmetric product of representation spheres. The filtration is more complicated than in the non-equivariant case, and already on the zeroth homotopy groups an interesting filtration of the augmentation ideal of the Burnside ring functor arises. Our method is by `global' homotopy theory, i.e., we study the simultaneous behaviour for all finite groups at once. The equivariant subquotients are no longer rationally trivial, nor even concentrated in dimension 0.
Information about the mailing list for this seminar may be found here.