A lower bound for the genus of self-amalgamation of Heegaard splittings

Fengling Li; Fengchun Lei

doi:10.4134/BKMS.2011.48.1.67

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(1): 67-77

Printed January 1, 2011

https://doi.org/10.4134/BKMS.2011.48.1.67

A lower bound for the genus of self-amalgamation of Heegaard splittings

Fengling Li and Fengchun Lei

Harbin Institute of Technology, Dalian University of Technology

Abstract

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Abstract

Let $M$ be a compact orientable closed 3-manifold, and $F$ a non-separating incompressible closed surface in $M$. Let $M^{'}=M-\eta(F)$, where $\eta(F)$ is an open regular neighborhood of $F$ in $M$. In the paper, we give a lower bound of genus of self-amalgamation of minimal Heegaard splitting $V^{'}\cup_{S^{'}}W^{'}$ of $M^{'}$ under some conditions on the distance of the Heegaard splitting.

Keywords: Heegaard distance, Heegaard genus, self-amalgamation

MSC numbers: 57M99