2025/12/08 by Neofytidis, Christoforos
Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals
paper · doi:10.48550/arxiv.2512.07238
openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
We show that all self-maps of non-zero degree of 3-manifolds not covered by S3 and of Thurston geometric 4-manifolds and their connected sums not covered by N#(#p≥0S2× S2)#(#q≥0\mathbb C P2), where N is an S2×\mathbb X2 or S3×\mathbb R manifold, are π1-injective. We thus determine when these maps induce π1-isomorphisms. The results in dimension three were previously established by Shicheng Wang. We give a uniform group theoretic proof in all cases based only on the residual finiteness of the fundamental groups for the π1-injectivity and then only on numerical invariants for the π1-isomorphisms.