New constructions and invariants of closed exotic 4-manifolds

2023/07/16 by Adam Simon Levine, Levine, Adam Simon, Tye Lidman +3 · 2 citations
Mathematics · Medicine · #57K18 #57K41 #57R58 #Advanced Combinatorial Mathematics #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2307.08130

openalex publication_date 2023/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• More Exotic \mathbbRP²-knots and Homotopy Spheres
• Distinguishing closed 4-manifolds by slicing

Related

• Open manifolds, Ozsvath-Szabo invariants and Exotic R⁴'s
• Exotic definite four-manifolds with non-trivial fundamental group
• New Exotic four-manifolds with ℤ/2ℤ fundamental group
• An introduction to exotic 4-manifolds
• Exotic 4-manifolds with signature zero