Invariance of tautological equations II: Gromov-Witten theory
Journal of the American Mathematical Society, Tome 22 (2009) no. 2, pp. 331-352

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-08-00616-4

Lee, Y.-P. 1

1 Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
@article{10_1090_S0894_0347_08_00616_4,
     author = {Lee, Y.-P.},
     title = {Invariance of tautological equations {II:} {Gromov-Witten} theory},
     journal = {Journal of the American Mathematical Society},
     pages = {331--352},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2009},
     doi = {10.1090/S0894-0347-08-00616-4},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-08-00616-4/}
}
TY  - JOUR
AU  - Lee, Y.-P.
TI  - Invariance of tautological equations II: Gromov-Witten theory
JO  - Journal of the American Mathematical Society
PY  - 2009
SP  - 331
EP  - 352
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-08-00616-4/
DO  - 10.1090/S0894-0347-08-00616-4
ID  - 10_1090_S0894_0347_08_00616_4
ER  - 
%0 Journal Article
%A Lee, Y.-P.
%T Invariance of tautological equations II: Gromov-Witten theory
%J Journal of the American Mathematical Society
%D 2009
%P 331-352
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-08-00616-4/
%R 10.1090/S0894-0347-08-00616-4
%F 10_1090_S0894_0347_08_00616_4
Lee, Y.-P. Invariance of tautological equations II: Gromov-Witten theory. Journal of the American Mathematical Society, Tome 22 (2009) no. 2, pp. 331-352. doi: 10.1090/S0894-0347-08-00616-4

[1] Arcara, D., Lee, Y.-P. Tautological equations in genus 2 via invariance constraints Bull. Inst. Math. Acad. Sin. (N.S.) 2007 1 27

[2] Coates, Tom, Givental, Alexander Quantum Riemann-Roch, Lefschetz and Serre Ann. of Math. (2) 2007 15 53

[3] Dijkgraaf, Robbert, Witten, Edward Mean field theory, topological field theory, and multi-matrix models Nuclear Phys. B 1990 486 522

[4] Faber, C., Pandharipande, R. Hodge integrals and Gromov-Witten theory Invent. Math. 2000 173 199

[5] Faber, C., Pandharipande, R. Relative maps and tautological classes J. Eur. Math. Soc. (JEMS) 2005 13 49

[6] Getzler, E. Topological recursion relations in genus 2 1998 73 106

[7] Getzler, Ezra The jet-space of a Frobenius manifold and higher-genus Gromov-Witten invariants 2004 45 89

[8] Givental, Alexander B. Gromov-Witten invariants and quantization of quadratic Hamiltonians Mosc. Math. J. 2001

[9] Givental, Alexander B. Symplectic geometry of Frobenius structures 2004 91 112

[10] Kontsevich, M., Manin, Yu. Gromov-Witten classes, quantum cohomology, and enumerative geometry Comm. Math. Phys. 1994 525 562

[11] Kontsevich, M., Manin, Yu. Relations between the correlators of the topological sigma-model coupled to gravity Comm. Math. Phys. 1998 385 398

[12] Lee, Y.-P. Invariance of tautological equations. I. Conjectures and applications J. Eur. Math. Soc. (JEMS) 2008 399 413

[13] Lee, Y.-P. Witten’s conjecture and the Virasoro conjecture for genus up to two 2006 31 42

Cité par Sources :