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- W1611384411 abstract "The ancestor Gromov--Witten invariants of a compact {Kahler} manifold $X$ can be organized in a generating function called the total ancestor potential of $X$. In this paper, we construct Hirota Quadratic Equations (HQE shortly) for the total ancestor potential of $C P^1$. The idea is to adopt the formalism developed in cite{G1,GM} to the mirror model of $C P^1$. We hope that the ideas presented here can be generalized to other manifolds as well. As a corollary, using the twisted loop group formalism from cite{G3}, we obtain a new proof of the following version of the Toda conjecture: the total descendant potential of $C P^1$ (known also as the partition function of the $C P^1$ topological sigma model) is a tau-function of the Extended Toda Hierarchy." @default.
- W1611384411 created "2016-06-24" @default.
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- W1611384411 date "2006-04-29" @default.
- W1611384411 modified "2023-09-27" @default.
- W1611384411 title "Gromov--Witten Theory of CP^1 and Integrable Hierarchies" @default.
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