Time: 09:30
Speaker: Grigory Solomadin (HSE Moscow)
Title: "Homotopy decomposition for quotients of moment-angle manifolds and its applications to cohomology"
Room: https://westernuniversity.zoom.us/s/93798234275, Passcode: 520011

Abstract: In this talk we present computational tools for singular and equivariant cohomology of orbit spaces for moment-angle complexes with respect to any closed subgroup in the naturally acting torus (quotients). The tools are the Bousfield-Kan spectral sequence collapse, commutation of cohomology and colimit, and the diagram of Koszul resolutions. These ideas stem from the recent homotopy decomposition for any such quotient obtained by the author joint with I. Limonchenko, and are motivated by previous works of Notbohm and Ray; M. Franz; Lambrechts, Tourchine and Volic.

We will discuss proofs and applications of this toolkit, namely: the new formulas for the equivariant cohomology ring for a certain class (*) of non-free quotients; the equivariant and singular (Hohster-type) cohomology ring and group, respectively; formulas for the quotients by coordinate tori; Eilenberg-Moore spectral sequence construction and collapse for (*); a comparison spectral sequence between EMSS and BKSS second pages.