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A real motivic v_1 selfmap

Geometry-Topology Seminar

Thursday, February 25, 2021 - 4:30pm

Ang Li

University of Kentucky

Location

University of Pennsylvania

via Zoom

The Zoom link is: https://upenn.zoom.us/j/97003688364. This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (mmerling@math.upenn.edu), Davi Maximo (dmaxim@math.upenn.edu) or Herman Gluck (gluck@math.upenn.edu).

Let C_2 be the group of order 2. We consider a nontrivial action of C_2 on the spectrum Y:=S/2 smash S/\eta. This can also be viewed as the complex points of a finite real-motivic spectrum. We will show that one of the classical v_1-self-maps of Y can be lifted to a C_2 equivariant self-map as well as a real-motivic self-map. Further, we will discuss that the cofiber of the self-map of the R-motivic lift of Y is a realization of the real-motivic Steenrod subalgebra A(1). We will also discuss the question of finding other realizations of A(1).
This is joint work with Prasit Bhattacharya and Bertrand Guillou.