Generalized Witten Genus and Vanishing Theorems
Differential Geometry
2012-04-16 v1 Algebraic Topology
Abstract
We construct a generalized Witten genus for spin manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin manifolds called string manifolds. We also construct a mod 2 analogue of the Witten genus for dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalized Witten genus and the mod 2 Witten genus on string and string (generalized) complete intersections in (product of) complex projective spaces respectively.
Keywords
Cite
@article{arxiv.1003.2325,
title = {Generalized Witten Genus and Vanishing Theorems},
author = {Qingtao Chen and Fei Han and Weiping Zhang},
journal= {arXiv preprint arXiv:1003.2325},
year = {2012}
}
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28 pages