Geography of irreducible 4-manifolds with order two fundamental group

2025/02/11 by Mihail Arabadji, Arabadji, Mihail, Porter Morgan +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2502.07689

openalex publication_date 2025/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a closed, oriented topological 4-manifold whose Euler characteristic and signature are denoted by e and σ. We show that if R has order two π₁, odd intersection form, and 2e + 3σ≥ 0, then for all but seven (e, σ) coordinates, R admits an irreducible smooth structure. We accomplish this by performing a variety of operations on irreducible simply-connected 4-manifolds to build 4-manifolds with order two π₁. These techniques include torus surgeries, symplectic fiber sums, rational blow-downs, and numerous constructions of Lefschetz fibrations, including a new approach to equivariant fiber summing.

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• Irreducible 4-manifolds with order two fundamental group and even intersection form
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