Generalized Witten Genus and Vanishing Theorems

Qingtao Chen; F. Han; W. Zhang

Generalized Witten Genus and Vanishing Theorems

Qingtao Chen
, F. Han
, W. Zhang

Department of Pure Mathematics

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

15 Citations (Scopus)

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 generalized Witten 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
Pages (from-to)	1-39
Number of pages	39
Journal	Journal of Differential Geometry
Volume	88
Issue number	1
Publication status	Published - May 2011

Cite this

@article{f2b2d469df524409b88c9fd553c4fd2e,

title = "Generalized Witten Genus and Vanishing Theorems",

abstract = "We construct a generalized Witten genus for spin\textasciicircum{}c manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin\textasciicircum{}c manifolds called string\textasciicircum{}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 generalized Witten genus and the mod 2 Witten genus on string\textasciicircum{}c and string (generalized) complete intersections in (product of) complex projective spaces respectively.",

author = "Qingtao Chen and F. Han and W. Zhang",

year = "2011",

month = may,

language = "English",

volume = "88",

pages = "1--39",

journal = "Journal of Differential Geometry",

issn = "0022-040X",

number = "1",

}

TY - JOUR

T1 - Generalized Witten Genus and Vanishing Theorems

AU - Chen, Qingtao

AU - Han, F.

AU - Zhang, W.

PY - 2011/5

Y1 - 2011/5

N2 - 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 generalized Witten genus and the mod 2 Witten genus on string^c and string (generalized) complete intersections in (product of) complex projective spaces respectively.

AB - 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 generalized Witten genus and the mod 2 Witten genus on string^c and string (generalized) complete intersections in (product of) complex projective spaces respectively.

M3 - Article

SN - 0022-040X

VL - 88

SP - 1

EP - 39

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 1

ER -

Generalized Witten Genus and Vanishing Theorems

Abstract

Fingerprint

Cite this