Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Invariance of tautological equations II: Gromov-Witten theory
HTML articles powered by AMS MathViewer

by Y.-P. Lee; with Appendix A by Y. Iwao; Y.-P. Lee PDF
J. Amer. Math. Soc. 22 (2009), 331-352 Request permission

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.
References
  • D. Arcara and Y.-P. Lee, Tautological equations in genus 2 via invariance constraints, Bull. Inst. Math. Acad. Sin. (N.S.) 2 (2007), no. 1, 1–27. MR 2294106
  • AL2 D. Arcara, Y.-P. Lee, Tautological equation in $\overline {M}_{3,1}$ via invariance constraints, math.AG/0503184, to appear in Canadian Mathematical Bulletin. AL3 D. Arcara, Y.-P. Lee, On independence of generators of the tautological rings, math.AG/0605488, to appear in Compositio Math.
  • Tom Coates and Alexander Givental, Quantum Riemann-Roch, Lefschetz and Serre, Ann. of Math. (2) 165 (2007), no. 1, 15–53. MR 2276766, DOI 10.4007/annals.2007.165.15
  • Robbert Dijkgraaf and Edward Witten, Mean field theory, topological field theory, and multi-matrix models, Nuclear Phys. B 342 (1990), no. 3, 486–522. MR 1072731, DOI 10.1016/0550-3213(90)90324-7
  • FSZ C. Faber, S. Shadrin, D. Zvonkine, Tautological relations and the $r$-spin Witten conjecture, arXiv:math/0612510.
  • C. Faber and R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math. 139 (2000), no. 1, 173–199. MR 1728879, DOI 10.1007/s002229900028
  • C. Faber and R. Pandharipande, Relative maps and tautological classes, J. Eur. Math. Soc. (JEMS) 7 (2005), no. 1, 13–49. MR 2120989, DOI 10.4171/JEMS/20
  • E. Getzler, Topological recursion relations in genus $2$, Integrable systems and algebraic geometry (Kobe/Kyoto, 1997) World Sci. Publ., River Edge, NJ, 1998, pp. 73–106. MR 1672112
  • Ezra Getzler, The jet-space of a Frobenius manifold and higher-genus Gromov-Witten invariants, Frobenius manifolds, Aspects Math., E36, Friedr. Vieweg, Wiesbaden, 2004, pp. 45–89. MR 2115766
  • Alexander B. Givental, Gromov-Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001), no. 4, 551–568, 645 (English, with English and Russian summaries). Dedicated to the memory of I. G. Petrovskii on the occasion of his 100th anniversary. MR 1901075, DOI 10.17323/1609-4514-2001-1-4-551-568
  • Alexander B. Givental, Symplectic geometry of Frobenius structures, Frobenius manifolds, Aspects Math., E36, Friedr. Vieweg, Wiesbaden, 2004, pp. 91–112. MR 2115767
  • GL A. Givental, Y.-P. Lee, unpublished.
  • M. Kontsevich and Yu. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), no. 3, 525–562. MR 1291244, DOI 10.1007/BF02101490
  • M. Kontsevich and Yu. Manin, Relations between the correlators of the topological sigma-model coupled to gravity, Comm. Math. Phys. 196 (1998), no. 2, 385–398. MR 1645019, DOI 10.1007/s002200050426
  • Y.-P. Lee, Invariance of tautological equations. I. Conjectures and applications, J. Eur. Math. Soc. (JEMS) 10 (2008), no. 2, 399–413. MR 2390329, DOI 10.4171/JEMS/115
  • ypL2 Y.-P. Lee, Witten’s conjecture, Virasoro conjecture, and invariance of tautological equations, math.AG/0311100.
  • Y.-P. Lee, Witten’s conjecture and the Virasoro conjecture for genus up to two, Gromov-Witten theory of spin curves and orbifolds, Contemp. Math., vol. 403, Amer. Math. Soc., Providence, RI, 2006, pp. 31–42. MR 2234883, DOI 10.1090/conm/403/07594
  • LP 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/ cT C. Teleman, The structure of 2D semi-simple field theories, arXiv:0712.0160. rV R. Vakil, The moduli space of curves and Gromov-Witten theory, math.AG/0602347.
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 14N35, 14H10
  • Retrieve articles in all journals with MSC (2000): 14N35, 14H10
Additional Information
  • Y.-P. Lee
  • Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
  • MR Author ID: 618293
  • Email: yplee@math.utah.edu
  • Y. Iwao
  • Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
  • Email: yshr19@gmail.com
  • Received by editor(s): May 30, 2006
  • Published electronically: September 24, 2008
  • Additional Notes: This research was partially supported by NSF and an AMS Centennial Fellowship
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 22 (2009), 331-352
  • MSC (2000): Primary 14N35, 14H10
  • DOI: https://doi.org/10.1090/S0894-0347-08-00616-4
  • MathSciNet review: 2476776