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Witten genus of generalized complete intersections in products of Grassmannians

Jian Zhou

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China

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and

Xiaobo Zhuang

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China

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https://doi.org/10.1142/S0129167X14500955Cited by:2 (Source: Crossref)

Abstract

By using the Milnor ring structure of the cohomology of Grassmannian, we prove a vanishing theorem of Witten genus for generalized string complete intersections in products of Grassmannian.

Keywords:

AMSC: 58J26, 14K25, 14M15

References

M. F. Atiyah and I. M. Singer, Ann. of Math. 87(3), 546 (1968). Crossref, Web of Science, Google Scholar
M. F. Atiyah and I. M. Singer, Ann. of Math. 93(1), 139 (1971). Crossref, Web of Science, Google Scholar
R. Bott and C. Taubes, J. Amer. Math. Soc. 2(1), 137 (1989). Crossref, Google Scholar
R. Bott and L. W. Tu , Differential Forms in Algebraic Topology ( Springer , New York , 1982 ) . Crossref, Google Scholar
K. Chandrasekharan , Elliptic Functions , Grundlehren der Mathematischen Wissenschaften 281 ( Springer-Verlag , Berlin , 1985 ) . Crossref, Google Scholar
Q. Chen and F. Han, Pacific J. Math. 234(2), 249 (2008). Crossref, Web of Science, Google Scholar
Q. Chen, F. Han and W. Zhang, J. Differential Geom. 88(1), 1 (2011). Crossref, Web of Science, Google Scholar
A. Dessai , The Witten Genus and S3-actions on Manifolds ( Fachbereich Mathematik, Universität Mainz , 1994 ) . Google Scholar
M. Förster, On the stolz conjecture for generalized complete intersections in irreducible, compact, Hermitian, symmetric spaces (Fachbereich Mathematik und Informatik, Dissertation, Universität Münster, Münster, 2007) . Google Scholar
W. Fulton , Intersection Theory ( Springer , New York , 1998 ) . Crossref, Google Scholar
P. Griffiths and J. Harris , Principles of Algebraic Geometry 52 ( John Wiley & Sons, Springer , New York , 2011 ) . Google Scholar
S. Guo and J. Zhou, International J. Math. 22(05), 695 (2011). Link, Web of Science, Google Scholar
F. Hirzebruch , Elliptic Genera of Level N for Complex Manifolds ( Max-Planck-Institut für Mathematik , Dordrecht , 1988 ) . Crossref, Google Scholar
F. Hirzebruch et al. , Manifolds and Modular Forms ( Friedrich Vieweg & Son Verlagsgesellschaft mbH , Braunschweig , 1992 ) . Crossref, Google Scholar
I. M. Krichever, Math. Notes 47(2), 132 (1990). Crossref, Web of Science, Google Scholar
H. B. Lawson Jr. and M.-L. Michelsohn , Spin Geometry Princeton Mathematical Series 38 ( Princeton University Press , New Jersey , 1989 ) . Google Scholar
A. Lichnerowicz , Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 33 , 187 ( 1962 ) . Google Scholar
K. Liu , J. Differential Geom. 41 , 343 ( 1995 ) . Crossref, Web of Science, Google Scholar
K. Liu, Topology 35(3), 617 (1996). Crossref, Web of Science, Google Scholar
X. Ma and J. Zhou, Int. J. Math. 16(10), 1131 (2005). Link, Web of Science, Google Scholar
J. W. Milnor , Characteristic Classes 76 ( Princeton University Press , New Jersey , 1974 ) . Crossref, Google Scholar
S. Stolz, Math. Ann. 304(1), 785 (1996). Crossref, Web of Science, Google Scholar
C. H. Taubes, Comm. Math. Phys. 122(3), 455 (1989). Crossref, Web of Science, Google Scholar
A. Tsikh , Multidimensional Residues and their Applications , Translations of Mathematical Monographs 103 ( American Mathematical Society , Providence, RI , 1992 ) . Crossref, Google Scholar
K. Waldorf, Spin structures on loop spaces that characterize string manifolds, preprint (2012) , arXiv:1209.1731 . Google Scholar
E. Witten, Elliptic Curves and Modular Forms in Algebraic Topology (Springer, Berlin, 1988) pp. 161–181. Crossref, Google Scholar
E. Witten, Geometry, Topology, Physics (International Press, Cambridge, MA, 1995) pp. 357–422. Google Scholar
J. Zhou, Introduction to Symmetric Functions (2003), http://faculty.math.tsinghua. edu.cn/jzhou/SymmetricF.pdf . Google Scholar