×

Remark on Witten’s modular forms. (English) Zbl 0673.57024

Summary: We give a simple proof of the modular invariance of a power series which E. Witten [Lect. Notes Math. 1326, 161-181 (1988)] 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.

MSC:

57R20 Characteristic classes and numbers in differential topology
11F11 Holomorphic modular forms of integral weight
57R75 \(\mathrm{O}\)- and \(\mathrm{SO}\)-cobordism
55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
58A12 de Rham theory in global analysis
PDFBibTeX XMLCite
Full Text: DOI