New constructions and invariants of closed exotic 4-manifolds

Adam Simon Levine; Tye Lidman; Lisa Piccirillo

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arXiv · 2307.08130

New constructions and invariants of closed exotic 4-manifolds

Adam Simon Levine·Tye Lidman·Lisa Piccirillo

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Abstract

In this article, we give new means of constructing and distinguishing closed exotic four-manifolds. Using Heegaard Floer homology, we define new closed four-manifold invariants that are distinct from the Seiberg--Witten and Bauer--Furuta invariants and can remain distinct in covers. Our constructions include exotic definite manifolds with fundamental group $\mathbb Z/2$, infinite families of exotic manifolds that are related by knot surgeries on Alexander polynomial 1 knots, and exotic manifolds that contain square-zero spheres.

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Adam Simon Levine, Tye Lidman, Lisa Piccirillo. 2023-07-16. New constructions and invariants of closed exotic 4-manifolds. https://arxiv.org/abs/2307.08130

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