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Gravitational Descendants and the Moduli Space of Higher Spin Curves

Tyler J. Jarvis·Takashi Kimura·Arkady Vaintrob
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Abstract

The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of $r$-spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a priori analog in the theory of Gromov-Witten invariants), in terms of the multiplicativity of the virtual class. We prove that the Descent Axiom holds in the convex case, and consequently in genus zero.

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Tyler J. Jarvis, Takashi Kimura, Arkady Vaintrob. 2000-11-22. Gravitational Descendants and the Moduli Space of Higher Spin Curves. https://arxiv.org/abs/math/0009066

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