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Haken spheres in the connected sum of two lens spaces

Published online by Cambridge University Press:  03 February 2005

FENGCHUN LEI
FENGCHUN LEI
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P.R. China. e-mail: fclei@hope.hit.edu.cn
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Abstract

A Haken sphere $S$ in a 3-manifold $M$ with a Heegaard splitting $V\cup_F W$ is a separating 2-sphere in $M$ which intersects the Heegaard surface $F$ only in an essential circle in $F$. We describe how any two Haken spheres in the genus 2 Heegaard splitting of connected sum of two lens spaces are related, which extends Scharlemann–Thompson's corresponding result on Haken spheres in genus 2 Heegaard splitting for $S^3$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 1 , January 2005 , pp. 97 - 105
Copyright
2005 Cambridge Philosophical Society

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