A group action on Losev-Manin cohomological field theories

Sergey Shadrin[1]; Dimitri Zvonkine[2]

  • [1] Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, Postbus 94248, 1090 GE Amsterdam, Nederland
  • [2] Institut mathématique de Jussieu, Université Paris VI, 175, rue du Chevaleret, 75013 Paris, France and Stanford University Department of Mathematics Building 380, Sloan Hall Stanford, California 94305, USA

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 7, page 2719-2743
  • ISSN: 0373-0956

Abstract

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We discuss an analog of the Givental group action for the space of solutions of the commutativity equation. There are equivalent formulations in terms of cohomology classes on the Losev-Manin compactifications of genus  moduli spaces; in terms of linear algebra in the space of Laurent series; in terms of differential operators acting on Gromov-Witten potentials; and in terms of multi-component KP tau-functions. The last approach is equivalent to the Losev-Polyubin classification that was obtained via dressing transformations technique.

How to cite

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Shadrin, Sergey, and Zvonkine, Dimitri. "A group action on Losev-Manin cohomological field theories." Annales de l’institut Fourier 61.7 (2011): 2719-2743. <http://eudml.org/doc/275514>.

@article{Shadrin2011,
abstract = {We discuss an analog of the Givental group action for the space of solutions of the commutativity equation. There are equivalent formulations in terms of cohomology classes on the Losev-Manin compactifications of genus $0$ moduli spaces; in terms of linear algebra in the space of Laurent series; in terms of differential operators acting on Gromov-Witten potentials; and in terms of multi-component KP tau-functions. The last approach is equivalent to the Losev-Polyubin classification that was obtained via dressing transformations technique.},
affiliation = {Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, Postbus 94248, 1090 GE Amsterdam, Nederland; Institut mathématique de Jussieu, Université Paris VI, 175, rue du Chevaleret, 75013 Paris, France and Stanford University Department of Mathematics Building 380, Sloan Hall Stanford, California 94305, USA},
author = {Shadrin, Sergey, Zvonkine, Dimitri},
journal = {Annales de l’institut Fourier},
keywords = {cohomological field theory; commutativity equation; Losev-Manin space; Givental’s group; Gromov-Witten theory; Kadomtsev-Petviashvili hierarchy; Frobenius manifolds; Losev-Manin compactification; Givental's group action},
language = {eng},
number = {7},
pages = {2719-2743},
publisher = {Association des Annales de l’institut Fourier},
title = {A group action on Losev-Manin cohomological field theories},
url = {http://eudml.org/doc/275514},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Shadrin, Sergey
AU - Zvonkine, Dimitri
TI - A group action on Losev-Manin cohomological field theories
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 7
SP - 2719
EP - 2743
AB - We discuss an analog of the Givental group action for the space of solutions of the commutativity equation. There are equivalent formulations in terms of cohomology classes on the Losev-Manin compactifications of genus $0$ moduli spaces; in terms of linear algebra in the space of Laurent series; in terms of differential operators acting on Gromov-Witten potentials; and in terms of multi-component KP tau-functions. The last approach is equivalent to the Losev-Polyubin classification that was obtained via dressing transformations technique.
LA - eng
KW - cohomological field theory; commutativity equation; Losev-Manin space; Givental’s group; Gromov-Witten theory; Kadomtsev-Petviashvili hierarchy; Frobenius manifolds; Losev-Manin compactification; Givental's group action
UR - http://eudml.org/doc/275514
ER -

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