PD₃-complexes bound

2021/09/21 by Hillman, Jonathan A.
#57M45 #57P10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2109.09947

Abstract

We show that every PD₃-complex P bounds a PD₄-pair (Z,P). If P is orientable we may assume that π₁(Z)=1. We show also that if P has a manifold 1-skeleton then it is homotopy equivalent to a closed 3-manifold, and that if the inclusion of Z into P induces an isomorphism on fundamental groups then π₁(Z) is a free group.

Related

• PD₄-complexes with π₂ a projective ℤ[π₁]-module
• Pro-p completions of PD_n-groups
• Homotopy types of 4-manifolds with 3-manifold fundamental groups
• Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π₁
• The Cayley isomorphism property for ℤ_p³ × ℤ_q