Rational homotopy theory of manifold complements and Smith ideals
Organizers
Speaker
Grisha Papayanov
Time
Thursday, November 13, 2025 2:00 PM - 3:00 PM
Venue
A3-4-101
Online
Zoom 928 682 9093
(BIMSA)
Abstract
Additively, the cohomology of the complement of an orientable submanifold in a compact orientable manifold could be calculated with the help of the Gysin sequence. However, multiplication and higher cohomology operations could not be extracted from it. Indeed, there exist homotopy equivalent pairs (compact manifold, submanifold) with homotopy non-equivalent complements. Using the homotopy theory of so-called Smith ideals in dg-algebras we show that, if the inclusion of submanifold induces an injection on the rational homology groups, the rational cochain algebra of the complement is determined by the rational homotopy type of the pair. Joint work with A. Gorinov.