Algebraic Topology Seminar
Monday, September 25, 2023 at 4:30pm to 6:00pm
Building 2, 131
182 MEMORIAL DR, Cambridge, MA 02139
Speaker: Hana Jia Kong (Harvard University)
Title: A deformation of Borel equivariant homotopy
Abstract: The real motivic stable homotopy category has a close connection to the C2-equivariant stable homotopy category. From a computational perspective, the real motivic computation can be viewed as a simpler version which "removes the negative cone" in the C2-equivariant stable homotopy groups. On the other hand, by work of Burklund–Hahn–Senger, one can build the completed Artin–Tate real motivic category from the completed C2-equivariant category using the deformation construction associated to the C2-effective filtration.
In work with Gabriel Angelini-Knoll, Mark Behrens, and Eva Belmont, we try to build an analog of this deformation story for a general finite group G. We give a new interpretation of the C2-effective filtration in the Borel equivariant category which generalizes for G. Using this new interpretation, the deformation construction gives a deformation of the Borel equivariant stable homotopy category for general finite groups.