# Gromov-Witten theory of locally conformally symplectic manifolds and the Fuller index

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Yakov Savelyev , University of Colima, Mexico
IAS Room S-101

We review the classical Fuller index which is a certain rational invariant count of closed orbits of a smooth vector field, and then explain how in the case of a Reeb vector field on a contact manifold $C$, this index can be equated to a Gromov-Witten invariant counting holomorphic tori in the locally conformally symplectic manifold $C \times S^1$. This leads us to prove a certain variant of the classical Seifert conjecture for the odd dimensional spheres.