Some sufficient conditions for heegaard genera to be additive under annulus sum

Li Fengling; Lei Fengchun; Yang Guoqiu

doi:10.7146/math.scand.a-19221

Some sufficient conditions for heegaard genera to be additive under annulus sum

Li Fengling
, Lei Fengchun
, Yang Guoqiu

School of Sciences

Dalian University of Technology

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

4 Scopus citations

Abstract

Let M_i be a compact orientable 3-manifold, and A_i an incompressible annulus on a component F_i of ∂M_i , i = 1, ₂. Suppose A₁ is separating on F₁ and A₂ is non-separating on F₂. Let M be the annulus sum of M₁ and M₂ along A₁ and A₂. In the present paper we show that if Mi has a Heegaard splitting Vi ≊Si Wi with Heegaard distance d(S_i ) ≥ ₂g(M_i ) + 5 for _i = 1, 2, then g(M) = g(M1) + g(M₂). Moreover, when g(F₂) ≥ 2, the minimal Heegaard splitting of M is unique up to isotopy.

Original language	English
Pages (from-to)	173-188
Number of pages	16
Journal	Mathematica Scandinavica
Volume	115
Issue number	2
DOIs	https://doi.org/10.7146/math.scand.a-19221
State	Published - 2014

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title = "Some sufficient conditions for heegaard genera to be additive under annulus sum",

abstract = "Let Mi be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of ∂Mi , i = 1, 2. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper we show that if Mi has a Heegaard splitting Vi ≊Si Wi with Heegaard distance d(Si ) ≥ 2g(Mi ) + 5 for i = 1, 2, then g(M) = g(M1) + g(M2). Moreover, when g(F2) ≥ 2, the minimal Heegaard splitting of M is unique up to isotopy.",

author = "Li Fengling and Lei Fengchun and Yang Guoqiu",

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doi = "10.7146/math.scand.a-19221",

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T1 - Some sufficient conditions for heegaard genera to be additive under annulus sum

AU - Fengling, Li

AU - Fengchun, Lei

AU - Guoqiu, Yang

PY - 2014

Y1 - 2014

N2 - Let Mi be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of ∂Mi , i = 1, 2. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper we show that if Mi has a Heegaard splitting Vi ≊Si Wi with Heegaard distance d(Si ) ≥ 2g(Mi ) + 5 for i = 1, 2, then g(M) = g(M1) + g(M2). Moreover, when g(F2) ≥ 2, the minimal Heegaard splitting of M is unique up to isotopy.

AB - Let Mi be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of ∂Mi , i = 1, 2. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper we show that if Mi has a Heegaard splitting Vi ≊Si Wi with Heegaard distance d(Si ) ≥ 2g(Mi ) + 5 for i = 1, 2, then g(M) = g(M1) + g(M2). Moreover, when g(F2) ≥ 2, the minimal Heegaard splitting of M is unique up to isotopy.

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JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

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ER -

Some sufficient conditions for heegaard genera to be additive under annulus sum

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