On maximal collections of essential non-spanning annuli in a simple compression body
Ming Li · Journal of Liaoning Normal University · 2009
Rubinstein-Scharlemann proved in 1999 that a maximal collection of essential annuli.in a handlebody of genus 2 consists of 1,2 or at most 3 annuli.Feng Chun Lei-JingYan Tang extended the above result in 2006 and proved that a maximal collection of essential annuli in a handlebody of genus n(n≥2) can contain at most 4n-5 annuli and 4n-5 is the least upper bound.XunBo Yin-Jing Yan Tang-Feng Chung Lei proved in 2009 that a maximal collection of essential annuli in a handlebody of genus n(n≥3) can contain at least 2 annuli and 2 is the greatest lower bound.In the present note,we show that a maximal collection of essential non-spanning annuli in a simple compression body could be 2 or 3.This partially extends the known results.