# U. Haifa Topology & Geometry seminar: Sunday, Mar. 6, 2022. Speaker: Greg Arone (University of Stockholm). “Title: Ext in the category of functors from Groups to abelian groups”

Time:  17:00 (Israel Time)

Location:  Room 614, Science & Education Building, University of Haifa

and on Zoom (see below)

https://us02web.zoom.us/rec/share/jtfNDNX5RaN1GdA09LGJykGM_nVmLaHW6dcKoTu5B-yUk5bDjL64Y-nSoQoJHyDI.vjEmMP1I3vyXjJpf

Abstract.

We consider the category of polynomial functors from finitely generated free groups to abelian groups. Favorite examples include exterior powers of abelianization, and the so called Passi functors, whose definition we will recall. Our main result says that the derived category of this category is equivalent to the category of excisive functors from pointed spaces to chain complexes. Under this equivalence, exterior powers of abelianization correspond to chains on reduced symmetric powers of spaces. Using this correspondence, one can calculate Ext groups in the functor category on a large scale.

Joint work with Marco Nervo.

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