Remark on Witten’s modular forms

Brylinski, Jean-Luc

doi:10.1090/S0002-9939-1989-0942631-1

Remark on Witten’s modular forms
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by Jean-Luc Brylinski PDF

Proc. Amer. Math. Soc. 105 (1989), 773-775 Request permission

Abstract:

We give a simple proof of the modular invariance of a power series which Witten [4] attaches to an even-dimensional closed manifold whose first Pontryagin class is torsion. The proof uses only the functional equation satisfied by classical theta functions.

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