Topological elliptic genera

Abstract: There is a classical notion of elliptic genera, which assigns Jacobi forms to SU-manifolds. In this talk, I explain my work with Ying-Hsuan Lin (arXiv:2412.02298) to give its homotopy-theoretical refinements and variants, which we call “topological elliptic genera”. The codomain becomes genuinely equivariant twisted Topological Modular Forms. In this talk, I explain the construction and physical idea behind, and discuss an application where we derive an interesting divisibility result of Euler numbers for Sp-manifolds. Also I explain a recent update with Tilman Bauer (in preparation) proving the surjectivity results of topological elliptic genera.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

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Topology and Geometry Seminar (Texas, Kansas)