Homotopy classification of 4-manifolds with 3-manifold fundamental group

2025/08/10 by Jonathan A. Hillman, Daniel Kasprowski, Hillman, Jonathan +5
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2508.07504

Abstract

We give a criterion on a group π and a homomorphism w \colon π→ C₂ under which closed 4-manifolds with fundamental group π and orientation character w are classified up to homotopy equivalence by their quadratic 2-types. We verify the criterion for a large class of 3-manifold groups and orientation characters, in particular for the fundamental group π of any closed, orientable 3-manifold whose finite subgroups are cyclic, provided w vanishes on every element of π of finite order. We deduce a homeomorphism classification of closed, orientable 4-manifolds with infinite dihedral fundamental group ℤ/2 * ℤ/2.

Related

• Homotopy types of 4-manifolds with 3-manifold fundamental groups
• 4-manifolds with a given boundary
• 4-manifolds with boundary and fundamental group ℤ
• Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π₁
• Homotopy invariance of higher signatures and 3-manifold groups