A Lower Bound of the Genus of a Self-Amalgamated 3-Manifolds

A Lower Bound of the Genus of a Self-Amalgamated 3-Manifolds

Year:    2011

Author:    Xu Li, Fengchun Lei

Communications in Mathematical Research , Vol. 27 (2011), Iss. 1 : pp. 47–52

Abstract

Let $M$ be a compact connected oriented 3-manifold with boundary, $Q_1, Q_2 ⊂ ∂M$ be two disjoint homeomorphic subsurfaces of $∂M$, and $h : Q_1 → Q_2$ be an orientation-reversing homeomorphism. Denote by $M_h$ or $M_{Q_1=Q_2}$ the 3-manifold obtained from $M$ by gluing $Q_1$ and $Q_2$ together via $h$. $M_h$ is called a self-amalgamation of $M$ along $Q_1$ and $Q_2$. Suppose $Q_1$ and $Q_2$ lie on the same component $F'$ of $∂M'$, and $F' − Q_1 ∪ Q_2$ is connected. We give a lower bound to the Heegaard genus of $M$ when $M'$ has a Heegaard splitting with sufficiently high distance.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2011-CMR-19105

Communications in Mathematical Research , Vol. 27 (2011), Iss. 1 : pp. 47–52

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    6

Keywords:    self-amalgamation distance Heegaard genus.

Author Details

Xu Li

Fengchun Lei