New constructions and invariants of closed exotic 4-manifolds

TL;DR

This paper introduces new methods for constructing and differentiating closed exotic 4-manifolds using novel invariants derived from Heegaard Floer homology, expanding the toolkit beyond traditional invariants.

Contribution

It develops new invariants from Heegaard Floer homology that distinguish exotic 4-manifolds and presents novel constructions including exotic definite manifolds and those related by knot surgeries.

Findings

New invariants from Heegaard Floer homology that differ from existing invariants.

Construction of exotic definite manifolds with fundamental group Z/2.

Infinite families of exotic manifolds related by knot surgeries.

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.