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Witten's conjecture, Virasoro conjecture, and invariance of tautological equations

Y. -P. Lee
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Abstract

The main goal of this paper is to prove the following two conjectures for genus up to two: 1. Witten's conjecture on the relations between higher spin curves and Gelfand--Dickey hierarchy. 2. Virasoro conjecture for target manifolds with conformal semisimple Frobenius manifolds. The main technique used in the proof is the invariance of tautological equations under loop group action.

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Y. -P. Lee. 2004-05-04. Witten's conjecture, Virasoro conjecture, and invariance of tautological equations. https://arxiv.org/abs/math/0311100

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