BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Manuel Rivera (Purdue) DTSTART:20201123T150000Z DTEND:20201123T160000Z DTSTAMP:20260423T052831Z UID:OATS/18 DESCRIPTION:Title: Th e coalgebra of chains and the fundamental group\nby Manuel Rivera (Pur due) as part of Online algebraic topology seminar\n\n\nAbstract\nRational homotopy theory tells us that simply connected spaces\, up to rational hom otopy equivalence\, may be classified algebraically by means of rational c ocommutative coalgebras (Quillen) or in the finite type case by rational d g commutative algebras (Sullivan). Goerss and Mandell proved versions of t hese results for fields of arbitrary characteristic by means of simplicial cocommutative coalgebras and E-infinity algebras\, respectively. The alge braic structures in these settings are considered up to quasi-isomorphism. \nIn this talk\, I will describe how to extend these results to spaces wit h arbitrary fundamental group.The key new observation is that the homotopy cocommutative coalgebraic structure of the chains on a space determines t he fundamental group in complete generality. The corresponding algebraic n otion of weak equivalence between coalgebras is drawn from Koszul duality. The end goal of this program is to completely understand homotopy types i n terms of algebraic “chain level” structure. This is joint work with M. Zeinalian and F. Wierstra.\n LOCATION:https://researchseminars.org/talk/OATS/18/ END:VEVENT END:VCALENDAR