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On DG-models for diagrams of spaces

组织者

马修·伯菲特 , 李京艳 , Pravin Kumar , 吴杰

演讲者

Nikita Golub

时间

2026年03月05日 15:00 至 16:00

地点

A3-4-301

线上

Zoom 518 868 7656 (BIMSA)

摘要

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.