Homology spheres bounding acyclic smooth manifolds and symplectic fillings

John B. Etnyre; Bülent Tosun

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arXiv · 2004.07405

Homology spheres bounding acyclic smooth manifolds and symplectic fillings

John B. Etnyre·Bülent Tosun

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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.

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John B. Etnyre, Bülent Tosun. 2020-04-16. Homology spheres bounding acyclic smooth manifolds and symplectic fillings. https://arxiv.org/abs/2004.07405

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