On the rank of $\pi_1(\mathrm{Symp}_0)$

Isaac Hasse-Armengol; Andrés Pedroza

On the rank of $\pi_1(\mathrm{Symp}_0)$

Symplectic Geometry 2022-03-04 v2 Algebraic Topology

Authors: Isaac Hasse-Armengol , Andrés Pedroza

Abstract

We show that for any positive integer $k$ there exists a closed symplectic $4$ -manifold $(M,\omega)$ , such that $H^1_\mathrm{dR}(M;\mathbb{R})$ is a $k$ -dimensional real vector space and its Flux group is equal to $H^1_\mathrm{dR}(M_1;\mathbb{Z})$ .

Keywords

symplectic 4-manifold flux group de rham cohomology rank of fundamental group symp0

Cite

@article{arxiv.2202.00215,
  title  = {On the rank of $\pi_1(\mathrm{Symp}_0)$},
  author = {Isaac Hasse-Armengol and Andrés Pedroza},
  journal= {arXiv preprint arXiv:2202.00215},
  year   = {2022}
}

Comments

Error in the section 2, in the construction of a loop of sympletic diffeomorphisms

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