Rectangle condition for compression bodies and 2-fold branched coverings

Jungsoo Kim; Jung Hoon Lee

doi:10.1142/S0218216512500782

Rectangle condition for compression bodies and 2-fold branched coverings

Jungsoo Kim^*
, Jung Hoon Lee

^*Corresponding author for this work

Department of Mathematics

Chung-Ang University

Research output: Contribution to journal › Journal article › peer-review

Abstract

We give the rectangle condition for strong irreducibility of Heegaard splittings of 3-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of 2-fold covering of S ³ branched along a link. The condition implies that any thin meridional level surface in the link complement is incompressible. We also show that the additivity of width holds for a composite knot satisfying the condition.

Original language	English
Article number	1250078
Journal	Journal of Knot Theory and its Ramifications
Volume	21
Issue number	8
DOIs	https://doi.org/10.1142/S0218216512500782
State	Published - 2012.07

Keywords

2-fold branched covering
generalized Heegaard splitting
Rectangle condition
thin position
width

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Access to Document

10.1142/S0218216512500782

Cite this

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title = "Rectangle condition for compression bodies and 2-fold branched coverings",

abstract = "We give the rectangle condition for strong irreducibility of Heegaard splittings of 3-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of 2-fold covering of S 3 branched along a link. The condition implies that any thin meridional level surface in the link complement is incompressible. We also show that the additivity of width holds for a composite knot satisfying the condition.",

keywords = "2-fold branched covering, generalized Heegaard splitting, Rectangle condition, thin position, width",

author = "Jungsoo Kim and Lee, \{Jung Hoon\}",

year = "2012",

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journal = "Journal of Knot Theory and its Ramifications",

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T1 - Rectangle condition for compression bodies and 2-fold branched coverings

AU - Kim, Jungsoo

AU - Lee, Jung Hoon

PY - 2012/7

Y1 - 2012/7

N2 - We give the rectangle condition for strong irreducibility of Heegaard splittings of 3-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of 2-fold covering of S 3 branched along a link. The condition implies that any thin meridional level surface in the link complement is incompressible. We also show that the additivity of width holds for a composite knot satisfying the condition.

AB - We give the rectangle condition for strong irreducibility of Heegaard splittings of 3-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of 2-fold covering of S 3 branched along a link. The condition implies that any thin meridional level surface in the link complement is incompressible. We also show that the additivity of width holds for a composite knot satisfying the condition.

KW - 2-fold branched covering

KW - generalized Heegaard splitting

KW - Rectangle condition

KW - thin position

KW - width

UR - https://www.scopus.com/pages/publications/84860537856

U2 - 10.1142/S0218216512500782

DO - 10.1142/S0218216512500782

M3 - Journal article

AN - SCOPUS:84860537856

SN - 0218-2165

VL - 21

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 8

M1 - 1250078

ER -

Rectangle condition for compression bodies and 2-fold branched coverings

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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