Singular maps on exotic 4-manifold pairs
Boldizsar Kalmar, Andras I. Stipsicz

TL;DR
This paper demonstrates that pairs of exotic 4-manifolds, which are topologically identical, can be distinguished by analyzing the topology of singular sets of smooth stable maps, utilizing Seiberg-Witten theory.
Contribution
It introduces a method to differentiate exotic 4-manifolds through the topology of singular sets in smooth maps, leveraging Seiberg-Witten invariants.
Findings
Exotic 4-manifold pairs can be distinguished by singular set topology.
Seiberg-Witten theory is effective in differentiating smooth structures.
Examples of such pairs are explicitly constructed.
Abstract
We show examples of pairs of smooth, compact, homeomorphic 4-manifolds, whose diffeomorphism types are distinguished by the topology of the singular sets of smooth stable maps defined on them. In this distinction we rely on results from Seiberg-Witten theory.
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