Journal of the American Mathematical Society

Author(s): Y.-P. Lee; with Appendix A by Y. Iwao and Y.-P. Lee
Journal: J. Amer. Math. Soc. 22 (2009), 331-352.
MSC (2000): Primary 14N35, 14H10
Posted: September 24, 2008
Retrieve article in: PDF

Abstract: The aim of Part II is to explore the technique of invariance of tautological equations in the realm of Gromov-Witten theory. The relationship between Gromov-Witten theory and the tautological rings of the moduli of curves is studied from Givental's point of view via deformation theory of semisimple axiomatic Gromov-Witten theory.

1.: D. Arcara, Y.-P. Lee, Tautological equations in genus two via invariance constraints, Bull. Inst. Math. Acad. Sin. (N.S.) 2 (2007), no. 1, 1-27. MR 2294106 (2008a:14068)
2.: D. Arcara, Y.-P. Lee, Tautological equation in $\overline{M}_{3,1}$ via invariance constraints, math.AG/0503184, to appear in Canadian Mathematical Bulletin.
3.: D. Arcara, Y.-P. Lee, On independence of generators of the tautological rings, math.AG/0605488, to appear in Compositio Math.
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13.: A. Givental, Y.-P. Lee, unpublished.
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16.: Y.-P. Lee, Invariance of tautological equations I: Conjectures and applications, J. Eur. Math. Soc. (JEMS) 10 (2008), no. 2, 399-413. MR 2390329
17.: Y.-P. Lee, Witten's conjecture, Virasoro conjecture, and invariance of tautological equations, math.AG/0311100.
18.: Y.-P. Lee, Witten's conjecture and Virasoro conjecture up to genus two, Gromov-Witten theory of spin curves and orbifolds, 31-42, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006. MR 2234883 (2007e:14089)
19.: Y.-P. Lee, R. Pandharipande, Frobenius manifolds, Gromov-Witten theory, and Virasoro constraints, in preparation. Materials needed for this paper are available from http://www.math.princeton.edu/˜rahulp/
20.: C. Teleman, The structure of 2D semi-simple field theories, arXiv:0712.0160.
21.: R. Vakil, The moduli space of curves and Gromov-Witten theory, math.AG/0602347.

Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 14N35, 14H10

Y.-P. Lee
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
Email: yplee@math.utah.edu

Y. Iwao
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
Email: yshr19@gmail.com

DOI: 10.1090/S0894-0347-08-00616-4
PII: S 0894-0347(08)00616-4
Keywords: Gromov--Witten theory, moduli of curves
Received by editor(s): May 30, 2006
Posted: September 24, 2008
Additional Notes: This research was partially supported by NSF and an AMS Centennial Fellowship
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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