Dear Colleagues and Students,
You are cordially invited to the Topology Seminar organized by the Department of Mathematics.
Speaker: Bob Oliver (Université Paris 13)
“The loop space homology of a small category”
Abstract: In an article published in 2009, Dave Benson described, for a ﬁnite group G, the mod p homology of the space Ω(BG^p) — the loop space of the p-completion of BG — in purely algebraic terms. In joint work with Carles Broto and Ran Levi, we have tried to better understand Benson’s result by generalizing it. Among other things, we showed that when C is a small category, |C| is its geometric realization, R is a commutative ring, and |C|+ R is a plus construction of |C| with respect to homologywith coeﬃcients in R, then H∗(Ω(|C|+ R);R) is the homology any chain complex of projective RC-modules that satisﬁes certain conditions. Benson’s theorem is then the special case where C is the category associated to a ﬁnite group G and R = Fp, so that p-completion appears as a special case of the plus construction.
Date: Monday, April 8, 2019
Place: Mathematics Seminar Room, SA – 141