Generalized witten genus and vanishing theorems

Qingtao Chen, Fei Han, Weiping Zhang

Research output: Contribution to journalArticle

Abstract

We construct a generalized Witten genus for spinc manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spinc manifolds called stringc 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 stringc and string (generalized) complete intersections in (product of) complex projective spaces respectively.

Original languageEnglish (US)
Pages (from-to)1-39
Number of pages39
JournalJournal of Differential Geometry
Volume88
Issue number1
DOIs
StatePublished - Jan 1 2011

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Vanishing Theorems
Genus
Complex Projective Space
Fourier Expansion
Complete Intersection
Modular Forms
Strings
Analogue

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Generalized witten genus and vanishing theorems. / Chen, Qingtao; Han, Fei; Zhang, Weiping.

In: Journal of Differential Geometry, Vol. 88, No. 1, 01.01.2011, p. 1-39.

Research output: Contribution to journalArticle

Chen, Qingtao ; Han, Fei ; Zhang, Weiping. / Generalized witten genus and vanishing theorems. In: Journal of Differential Geometry. 2011 ; Vol. 88, No. 1. pp. 1-39.
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