Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π₁

2021/08/12 by Hongbin Sun, Zhongzi Wang, Sun, Hongbin +1
Mathematics · #20J06 #57M05 #57N10 #57N13 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2108.05784

openalex publication_date 2021/08/12 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that any closed orientable 3-manifold M other than #^k S¹× S² and S³ satisfies the following properties: (1) For any compact orientable 4-manifold N bounded by M, the inclusion does not induce an isomorphism on their fundamental groups π₁. (2) For any map f:M→ N from M to a closed orientable 4-manifold N, f does not induce an isomorphism on π₁. Relevant results on higher dimensional manifolds are also obtained.

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