Families of nondiffeomorphic 4-manifolds with the same Seiberg-Witten invariants

TL;DR

This paper constructs infinite families of non-diffeomorphic symplectic 4-manifolds that share identical Seiberg-Witten invariants, expanding understanding of 4-manifold classification.

Contribution

It introduces a method to produce infinite families of nondiffeomorphic symplectic 4-manifolds with identical Seiberg-Witten invariants using knot surgery and covering techniques.

Findings

Existence of infinite families of such 4-manifolds.

These manifolds are non-simply connected.

They share the same Seiberg-Witten invariants.

Abstract

In this article, we show that, at least for non-simply connected case, there exist an infinite family of nondiffeomorphic symplectic 4-manifolds with the same Seiberg-Witten invariants. The main techniques are knot surgery and a covering method developed in Fintushel and Stern's paper (Geometry and Topology, 1999).