Note on primitive disk complexes

Sangbum Cho; Jung Hoon Lee

doi:10.1016/j.topol.2023.108521

Note on primitive disk complexes

Sangbum Cho
, Jung Hoon Lee^*

^*Corresponding author for this work

Department of Mathematics

Hanyang University

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

1 Scopus citations

Abstract

Given a Heegaard splitting of the 3-sphere, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting, spanned by the vertices of primitive disks. It is an open question whether the primitive disk complex is connected or not when the genus of the splitting is greater than three. In this note, we prove that a quotient of the primitive disk complex, called the homotopy primitive disk complex, is connected.

Original language	English
Article number	108521
Journal	Topology and its Applications
Volume	332
DOIs	https://doi.org/10.1016/j.topol.2023.108521
State	Published - 2023.06.1

Keywords

Disk complex
Heegaard splitting
Primitive disk

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1016/j.topol.2023.108521

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title = "Note on primitive disk complexes",

abstract = "Given a Heegaard splitting of the 3-sphere, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting, spanned by the vertices of primitive disks. It is an open question whether the primitive disk complex is connected or not when the genus of the splitting is greater than three. In this note, we prove that a quotient of the primitive disk complex, called the homotopy primitive disk complex, is connected.",

keywords = "Disk complex, Heegaard splitting, Primitive disk",

author = "Sangbum Cho and Lee, \{Jung Hoon\}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2023",

month = jun,

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doi = "10.1016/j.topol.2023.108521",

language = "English",

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journal = "Topology and its Applications",

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T1 - Note on primitive disk complexes

AU - Cho, Sangbum

AU - Lee, Jung Hoon

PY - 2023/6/1

Y1 - 2023/6/1

N2 - Given a Heegaard splitting of the 3-sphere, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting, spanned by the vertices of primitive disks. It is an open question whether the primitive disk complex is connected or not when the genus of the splitting is greater than three. In this note, we prove that a quotient of the primitive disk complex, called the homotopy primitive disk complex, is connected.

AB - Given a Heegaard splitting of the 3-sphere, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting, spanned by the vertices of primitive disks. It is an open question whether the primitive disk complex is connected or not when the genus of the splitting is greater than three. In this note, we prove that a quotient of the primitive disk complex, called the homotopy primitive disk complex, is connected.

KW - Disk complex

KW - Heegaard splitting

KW - Primitive disk

UR - https://www.scopus.com/pages/publications/85152116802

U2 - 10.1016/j.topol.2023.108521

DO - 10.1016/j.topol.2023.108521

M3 - Journal article

AN - SCOPUS:85152116802

SN - 0166-8641

VL - 332

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 108521

ER -

Note on primitive disk complexes

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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