# Invertible cohomological field theories and Weil-Petersson volumes

Annales de l'institut Fourier (2000)

- Volume: 50, Issue: 2, page 519-535
- ISSN: 0373-0956

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topManin, Yuri I., and Zograf, Peter. "Invertible cohomological field theories and Weil-Petersson volumes." Annales de l'institut Fourier 50.2 (2000): 519-535. <http://eudml.org/doc/75428>.

@article{Manin2000,

abstract = {We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande. From this formula we derive an asymptotical expression for the Weil–Petersson volume as conjectured by C. Itzykson. We also discuss a topological interpretation of the genus expansion formula of Itzykson–Zuber, as well as a related bialgebra acting upon quantum cohomology as a complex version of the classical path groupoid.},

author = {Manin, Yuri I., Zograf, Peter},

journal = {Annales de l'institut Fourier},

keywords = {moduli spaces; operads; Weil-Petersson volumes; cohomological field theories; Schur polynomials; stationary phase method; Virasoro constraints; potential; quantum cohomology; KdV equation},

language = {eng},

number = {2},

pages = {519-535},

publisher = {Association des Annales de l'Institut Fourier},

title = {Invertible cohomological field theories and Weil-Petersson volumes},

url = {http://eudml.org/doc/75428},

volume = {50},

year = {2000},

}

TY - JOUR

AU - Manin, Yuri I.

AU - Zograf, Peter

TI - Invertible cohomological field theories and Weil-Petersson volumes

JO - Annales de l'institut Fourier

PY - 2000

PB - Association des Annales de l'Institut Fourier

VL - 50

IS - 2

SP - 519

EP - 535

AB - We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande. From this formula we derive an asymptotical expression for the Weil–Petersson volume as conjectured by C. Itzykson. We also discuss a topological interpretation of the genus expansion formula of Itzykson–Zuber, as well as a related bialgebra acting upon quantum cohomology as a complex version of the classical path groupoid.

LA - eng

KW - moduli spaces; operads; Weil-Petersson volumes; cohomological field theories; Schur polynomials; stationary phase method; Virasoro constraints; potential; quantum cohomology; KdV equation

UR - http://eudml.org/doc/75428

ER -

## References

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