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arXiv · 2212.07882

Fundamental groups of rationally connected symplectic manifolds

Alex Pieloch
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Abstract

We show that the fundamental group of every enumeratively rationally connected closed symplectic manifold is finite. In other words, if a closed symplectic manifold has a non-zero Gromov-Witten invariant with two point insertions, then it has finite fundamental group. We also show that if the spherical homology class associated to such a non-zero Gromov-Witten invariant is holomorphically indecomposable, then the rational second homology of the symplectic manifold has rank one.

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Alex Pieloch. 2022-12-15. Fundamental groups of rationally connected symplectic manifolds. https://doi.org/10.1112/s0010437x25007456

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