A lower bound of genus of amalgamations of heegaard splittings

Fengchun Lei; Guoqiu Yang

doi:10.1017/S030500410800203X

A lower bound of genus of amalgamations of heegaard splittings

Fengchun Lei^*
, Guoqiu Yang

^*Corresponding author for this work

School of Sciences

Dalian University of Technology

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In the paper, we give a lower bound on the genus of an amalgamation of two Heegaard splittings V1, S1, W1 for M1 and V2, S2, W2 for M2 along boundary components F1 and F2 under some conditions on the distances of the factor Heegaard splittings. A direct consequence is that under some circumstances, g(M) = g(M1) + g(M2) g(F) holds, and another is that under some circumstances we have a better lower bound.

Original language	English
Pages (from-to)	615-623
Number of pages	9
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	146
Issue number	3
DOIs	https://doi.org/10.1017/S030500410800203X
State	Published - May 2009

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abstract = "In the paper, we give a lower bound on the genus of an amalgamation of two Heegaard splittings V1, S1, W1 for M1 and V2, S2, W2 for M2 along boundary components F1 and F2 under some conditions on the distances of the factor Heegaard splittings. A direct consequence is that under some circumstances, g(M) = g(M1) + g(M2) g(F) holds, and another is that under some circumstances we have a better lower bound.",

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AB - In the paper, we give a lower bound on the genus of an amalgamation of two Heegaard splittings V1, S1, W1 for M1 and V2, S2, W2 for M2 along boundary components F1 and F2 under some conditions on the distances of the factor Heegaard splittings. A direct consequence is that under some circumstances, g(M) = g(M1) + g(M2) g(F) holds, and another is that under some circumstances we have a better lower bound.

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A lower bound of genus of amalgamations of heegaard splittings

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