Minimal Sullivan algebra and its realization
Organizers
Speaker
Time
Thursday, October 10, 2024 2:00 PM - 4:00 PM
Venue
A3-2a-302
Online
Zoom 482 240 1589
(BIMSA)
Abstract
Sullivan's minimal model and realization identity the rational homotopy type of spaces and the quasi-isomorphism classes of differential graded algebras, under the assumptions of being simply-connected and having finite type cohomology. However, in the general case, counterexamples arise, and there remain unexplored areas. We prove that a minimal Sullivan algebra is a model of its realization if and only if its cohomology is of finite type. On the other hand, finite type cohomology is a necessary condition for a space to have its homotopy groups represented by its minimal model in a particular manner.