Generalized witten genus and vanishing theorems

Qingtao Chen; Fei Han; Weiping Zhang

doi:10.4310/jdg/1317758867

Generalized witten genus and vanishing theorems

Qingtao Chen, Fei Han, Weiping Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a generalized Witten genus for spin^c manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin^c manifolds called string^c manifolds. We also construct a mod 2 analogue of the Witten genus for 8k+2 dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalizedWitten genus and the mod 2 Witten genus on string^c and string (generalized) complete intersections in (product of) complex projective spaces respectively.

Original language	English (US)
Pages (from-to)	1-39
Number of pages	39
Journal	Journal of Differential Geometry
Volume	88
Issue number	1
DOIs	https://doi.org/10.4310/jdg/1317758867
State	Published - May 2011

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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Generalized witten genus and vanishing theorems

Abstract

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