Kernels of splitting homomorphisms

2022/04/17 by Michael R. Klug, Klug, Michael R.
Mathematics · #57K30 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2204.08041

openalex publication_date 2022/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lei and Wu have given a description of the second homotopy group of a closed orientable 3-manifold in terms of the kernels of the epimorphisms from the fundamental group of a Heegaard splitting surface onto the fundamental groups of the two handlebody sides. In this note, we give a geometric derivation of this result and collect some observations about the relation between the various groups and the topology of the 3-manifold and the Heegaard splitting.

Related

• The space of Heegaard Splittings
• Subgroups of mapping class groups related to Heegaard splittings and bridge decompositions
• Automorphisms of the three-torus preserving a genus three Heegaard splitting
• Handlebody-preserving finite group actions on Haken manifolds with Heegaard genus two
• Mapping class groups of medium distance Heegaard splittings