Formality of DGCAs and Highly Connected Manifolds -- L. Schwachhöfer (TU Dortmund), PHK 04.11.2026

Title: Formality of DGCAs and Highly Connected Manifolds (In memory of Hông Vân Lê) Speaker: Lorenz Schwachhöfer (TU Dortmund) Abstract: A closed manifold is called formal if its de Rham algebra is quasi-isomorphic to its cohomology algebra. In this case, its real homotopy type is determined by the cup product alone. For highly connected manifolds, formality is governed by a hierarchy of results and invariants, including Miller’s theorem, the Bianchi–Massey tensor introduced by Crowley and Nordström, and subsequent refinements. I will explain how Hodge theory organizes this hierarchy into a systematic framework, following a line of research developed by Hông Vân Lê and her collaborators - including Fiorenza, Kawai, and myself - and culminating in her recent stratification by “isotopy modulo k.” I will also discuss a more recent, alternative approach due to N. Otto. Working entirely with explicit Sullivan models, this approach produces new examples of non-formal manifolds whose non-formality is not detected by the Bianchi–Massey tensor. Talk given at the Prague-Hradec Králové seminar on Cohomology in algebra, geometry, physics and statistics: https://www.math.cas.cz/index.php/eve... https://researchseminars.org/talk/PHK...