superalgebra and (synthetic ) supergeometry
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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(2,1)-dimensional Euclidean field theories?
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 $(2|1)$-dimensional EFT is a modular form. Hence $(2|1)$-dimensional EFTs do yield the correct cohomology ring of tmf over the point.
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Created on September 24, 2009 at 15:17:55. See the history of this page for a list of all contributions to it.