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modular forms from partition functions

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This is a sub-entry of geometric models for elliptic cohomology and A Survey of Elliptic Cohomology

See there for background and context.

This entry here is about the fact and its derivation that the partition function of a (2,1)-dimensional Euclidean field theories is a modular form.

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Contents

Idea

As described at (2,1)-dimensional Euclidean field theories and tmf, the idea is that (2,1)-dimensional Euclidean field theories are a geometric model for tmf cohomology theory.

While there is no complete proof of this so far, here we discuss the construction and proof – due to Stephan Stolz and Peter Teichner – for the situation over the point: the partition function of a (2|1)(2|1)-dimensional EFT is a modular form. Hence (2|1)(2|1)-dimensional EFTs do yield the correct cohomology ring of tmf over the point.

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Created on September 24, 2009 15:21:39 by Urs Schreiber (195.37.209.182)