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The C_2 effective spectral sequence and the homotopy of ko_{C_2}

Banff International Research Station for Mathematical Innovation and Discovery

By work of Voevodsky, the slice filtration in motivic homotopy theory provides a powerful tool for computing homotopy groups of motivic spectra. In this talk, I will describe the motivic slice filtration and the effective slice spectral sequence it produces. Then I will discuss how the motivic effective slice spectral sequence gives rise to a spectral sequence in $C_2$ equivariant homotopy theory. One of the main applications is computing the homotopy groups of $ko_{C_2}$, the connective $C_2$ equivariant $K$ theory. This gives a reproof of work by Guillou-Hill-Isaksen-Ravenel that computes homotopy of $ko_{C_2}$ using equivariant Adams spectral sequence.

Mathematics; Category theory; homological algebra; K-theory; Algebraic topology

video/mp4

Author affiliation: University of Chicago

2020-09-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76112

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/