Saved in:
Bibliographic Details
Main Author: Taylor, Scott A.
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2006.07198
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of 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.