A lower bound for the genus of self-amalgamation of Heegaard splittings
Bull. Korean Math. Soc. 2011 Vol. 48, No. 1, 67-77
Printed January 1, 2011
Fengling Li and Fengchun Lei
Harbin Institute of Technology, Dalian University of Technology
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
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