Reduction of bridge positions along bridge disks

Jung Hoon Lee

doi:10.1016/j.topol.2017.03.012

Reduction of bridge positions along bridge disks

Jung Hoon Lee

Department of Mathematics

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

3 Scopus citations

Abstract

We consider a reduction of a knot in a bridge position along two disjoint bridge disks D₁ and D₂. Suppose that a reduction of the knot along any subset of {D₁,D₂} results in a bridge position, where we get two distinct new bridges after the reduction along D₁∪D₂. We show that there are two disjoint bridge disks E₁ and E₂ such that (D₁,E₁) and (D₂,E₂) are cancelling pairs and (D₁∪E₁)∩(D₂∪E₂)=∅.

Original language	English
Pages (from-to)	50-59
Number of pages	10
Journal	Topology and its Applications
Volume	223
DOIs	https://doi.org/10.1016/j.topol.2017.03.012
State	Published - 2017.06.1

Keywords

Bridge disk
Bridge splitting
Cancelling pair

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Access to Document

10.1016/j.topol.2017.03.012

Cite this

@article{c4f4aa9b27624221bbc234d6b06f2c9e,

title = "Reduction of bridge positions along bridge disks",

abstract = "We consider a reduction of a knot in a bridge position along two disjoint bridge disks D1 and D2. Suppose that a reduction of the knot along any subset of \{D1,D2\} results in a bridge position, where we get two distinct new bridges after the reduction along D1∪D2. We show that there are two disjoint bridge disks E1 and E2 such that (D1,E1) and (D2,E2) are cancelling pairs and (D1∪E1)∩(D2∪E2)=∅.",

keywords = "Bridge disk, Bridge splitting, Cancelling pair",

author = "Lee, \{Jung Hoon\}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

month = jun,

day = "1",

doi = "10.1016/j.topol.2017.03.012",

language = "English",

volume = "223",

pages = "50--59",

journal = "Topology and its Applications",

issn = "0166-8641",

}

TY - JOUR

T1 - Reduction of bridge positions along bridge disks

AU - Lee, Jung Hoon

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We consider a reduction of a knot in a bridge position along two disjoint bridge disks D1 and D2. Suppose that a reduction of the knot along any subset of {D1,D2} results in a bridge position, where we get two distinct new bridges after the reduction along D1∪D2. We show that there are two disjoint bridge disks E1 and E2 such that (D1,E1) and (D2,E2) are cancelling pairs and (D1∪E1)∩(D2∪E2)=∅.

AB - We consider a reduction of a knot in a bridge position along two disjoint bridge disks D1 and D2. Suppose that a reduction of the knot along any subset of {D1,D2} results in a bridge position, where we get two distinct new bridges after the reduction along D1∪D2. We show that there are two disjoint bridge disks E1 and E2 such that (D1,E1) and (D2,E2) are cancelling pairs and (D1∪E1)∩(D2∪E2)=∅.

KW - Bridge disk

KW - Bridge splitting

KW - Cancelling pair

UR - https://www.scopus.com/pages/publications/85016442246

U2 - 10.1016/j.topol.2017.03.012

DO - 10.1016/j.topol.2017.03.012

M3 - Journal article

AN - SCOPUS:85016442246

SN - 0166-8641

VL - 223

SP - 50

EP - 59

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Reduction of bridge positions along bridge disks

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

Other files and links

Cite this