TMF-cohomology via 2-dimensional QFTs

Abstract: Topological modular form theory is a generalized cohomology theory whose coefficient ring TMF^*(point) is rationally isomorphic to the ring of integral modular forms. Modular forms also show up as partition functions of suitable 2-dimensional QFTs. For example, the Witten genus W(X) of a closed manifold X is an integral modular form, provided X is a spin manifold and the first Pontryagin class of X is trivial. This led to the question whether the corresponding spectrum TMF can be constructed in terms of 2D field theories.

In this talk I will recall a result of Teichner and myself according to which the partition function of a supersymmetric 2D Euclidean field theory is an integral modular form, as well as a Conjecture expressing the spaces which form the spectrum TMF as spaces of supersymmetric 2D field theories.

algebraic geometrydifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Boston University Geometry/Physics Seminar

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