Kernels of splitting homomorphisms

Michael R. Klug

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arXiv · 2204.08041

Kernels of splitting homomorphisms

Michael R. Klug

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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.

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Michael R. Klug. 2022-04-17. Kernels of splitting homomorphisms. https://arxiv.org/abs/2204.08041

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