Minimal Sullivan algebra and its realization
演讲者
时间
2024年10月10日 14:00 至 16:00
地点
A3-2a-302
线上
Zoom 482 240 1589
(BIMSA)
摘要
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.