Equivariant Heegaard genus of reducible 3-manifolds

Fuente: arXiv
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Autor principal: Taylor, Scott A.
Formato: Preprint
Publicado: 2020
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author Taylor, Scott A.
author_facet Taylor, Scott A.
contents The equivariant Heegaard genus of a 3-manifold $M$ with the action of a finite group $G$ of diffeomorphisms is the smallest genus of an equivariant Heegaard splitting for $M$. Although a Heegaard splitting of a reducible manifold is reducible and although if $M$ is reducible, there is an equivariant essential sphere, we show that equivariant Heegaard genus may be super-additive, additive, or sub-additive under equivariant connected sum. Using a thin position theory for 3-dimensional orbifolds, we establish sharp bounds on the equivariant Heegaard genus of reducible manifolds, similar to those known for tunnel number.
format Preprint
id arxiv_https___arxiv_org_abs_2006_07198
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Equivariant Heegaard genus of reducible 3-manifolds
Taylor, Scott A.
Geometric Topology
The equivariant Heegaard genus of a 3-manifold $M$ with the action of a finite group $G$ of diffeomorphisms is the smallest genus of an equivariant Heegaard splitting for $M$. Although a Heegaard splitting of a reducible manifold is reducible and although if $M$ is reducible, there is an equivariant essential sphere, we show that equivariant Heegaard genus may be super-additive, additive, or sub-additive under equivariant connected sum. Using a thin position theory for 3-dimensional orbifolds, we establish sharp bounds on the equivariant Heegaard genus of reducible manifolds, similar to those known for tunnel number.
title Equivariant Heegaard genus of reducible 3-manifolds
topic Geometric Topology
url https://arxiv.org/abs/2006.07198