Homology spheres bounding acyclic smooth manifolds and symplectic fillings

John B. Etnyre; Bülent Tosun

Homology spheres bounding acyclic smooth manifolds and symplectic fillings

Geometric Topology 2021-05-18 v2 Symplectic Geometry

Authors: John B. Etnyre , Bülent Tosun

Abstract

In this paper, we collect various structural results to determine when an integral homology $3$ --sphere bounds an acyclic smooth $4$ --manifold, and when this can be upgraded to a Stein manifold. In a different direction we study whether smooth embedding of connected sums of lens spaces in $\mathbb{C}^2$ can be upgraded to a Stein embedding, and determined that this never happens.

Keywords

integral homology 3-sphere acyclic smooth 4-manifold stein manifold lens spaces connected sum stein embedding

Cite

@article{arxiv.2004.07405,
  title  = {Homology spheres bounding acyclic smooth manifolds and symplectic fillings},
  author = {John B. Etnyre and Bülent Tosun},
  journal= {arXiv preprint arXiv:2004.07405},
  year   = {2021}
}

Comments

14 pages. V2: minor referee's corrections, suggestions and bibliographic updates. This version to appear in Michigan Mathematical Journal

Homology spheres bounding acyclic smooth manifolds and symplectic fillings

Abstract

Keywords

Cite

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