BIMSA > BIMSA Topology Seminar On DG-models for diagrams of spaces
On DG-models for diagrams of spaces
Organizers
Matthew Burfitt , Jingyan Li , Pravin Kumar , Jie Wu
Speaker
Nikita Golub
Time
Thursday, March 5, 2026 3:00 PM - 4:00 PM
Venue
A3-4-301
Online
Zoom 518 868 7656 (BIMSA)
Abstract
In this seminar we extend rational homotopy theory to presheaves of spaces, generalizing Sullivan's minimal models to diagrams of spaces. Two types of DG-minimal models are introduced: algebraically minimal (based on decomposability of differentials) and geometrically minimal (dual to Postnikov towers), which are generally distinct, to the contsrast of classical theory. Their equivalence is obstructed by the rational cohomological dimension of the indexing category, yielding a new "algebraicity" property akin to formality. Applications include criteria for splitting H-space diagrams into products of Eilenberg–MacLane diagrams and encoding real homotopy types of smooth manifold diagrams via de Rham complexes. We also show that real equivariant homotopy types of equivariant isometries between Riemann G-manifolds are determined by cohomology of fixed point submanifolds.