Brylinski, Jean-Luc Remark on Witten’s modular forms. (English) Zbl 0673.57024 Proc. Am. Math. Soc. 105, No. 3, 773-775 (1989). 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. Cited in 1 Document 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 Keywords:Witten’s modular forms; even-dimensional closed manifold; first Pontryagin class; theta functions PDFBibTeX XMLCite \textit{J.-L. Brylinski}, Proc. Am. Math. Soc. 105, No. 3, 773--775 (1989; Zbl 0673.57024) Full Text: DOI