Gromov-Witten invariants of Riemann-Finsler manifolds
Yasha Savelyev
Yasha Savelyev
Sep 2023
0被引用
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摘要原文
We define a $\mathbb{Q}$-valued deformation invariant of certain complete Riemann-Finsler manifolds. We use this to prove (possibly non-compact but complete) fibration generalizations of Preissman's theorem on non-existence of negative sectional curvature metrics on compact products. In addition we prove that every non-positive rational number is the value of this invariant for some Riemannian manifold. We also prove that sky catastrophes of smooth dynamical systems are not geodesible by a certain class of complete Riemann-Finsler metrics, in particular by Riemannian metrics with non-positive sectional curvature. This partially answers a question of Fuller and gives important examples for our theory here. In a sister paper ~\cite{cite_SavelyevEllipticCurvesLcs}, we study a direct generalization of this metric invariant, by lifting the count of geodesics to a Gromov-Witten count of elliptic curves in an associated locally conformally symplectic manifold.
