Generalized witten genus and vanishing theorems

Qingtao Chen, Fei Han, Weiping Zhang

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - May 2011

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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