A group action on Losev-Manin cohomological field theories

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.

21 pages, 9 figures

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• Tautological relations and the r-spin Witten conjecture
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• Givental symmetries of Frobenius manifolds and multi-component KP tau-functions
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Cited by in corpus (7)

• Givental graphs and inversion symmetry
• Flat F-manifolds, F-CohFTs, and integrable hierarchies
• Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebras
• A remark on deformations of Hurwitz Frobenius manifolds
• Riemann-Hilbert-Birkhoff inverse problem for semisimple flat $F$-manifolds, and convergence of oriented associativity potentials
• Generalized cohomological field theories in the higher order formalism
• Reconnectads