Degree of roots of disk twists on 3-dimensional handlebodies

Susumu Hirose, Naoyuki Monden

Research output: Contribution to journalArticle

Abstract

Margalit and Schleimer (Geom Topol 13(3):1495-1497, 2009) discovered a nontrivial root of the Dehn twist about a nonseparating curve on a closed oriented connected surface. McCullough and Rajeevsarathy (Geom Dedicata 151(1):397-409, 2011) and Monden (Rocky Mt J Math, to appear) obtained the evaluation of the degrees of roots of Dehn twists. In this paper, we discuss existence and degrees of homeomorphisms whose power is equal to disk twist about a nonseparating disk in the mapping class group of the 3-dimensional handlebody.

Original languageEnglish
Pages (from-to)73-82
Number of pages10
JournalGeometriae Dedicata
Volume164
Issue number1
DOIs
Publication statusPublished - Jun 1 2013
Externally publishedYes

Fingerprint

Dehn Twist
Handlebody
Twist
Roots
Mapping Class Group
Closed
Curve
Evaluation

Keywords

  • 3-Dimensional handlebody
  • Disk twist
  • Mapping class group
  • Root

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Degree of roots of disk twists on 3-dimensional handlebodies. / Hirose, Susumu; Monden, Naoyuki.

In: Geometriae Dedicata, Vol. 164, No. 1, 01.06.2013, p. 73-82.

Research output: Contribution to journalArticle

@article{e191285179b64c02a8196cdb9f57e3e8,
title = "Degree of roots of disk twists on 3-dimensional handlebodies",
abstract = "Margalit and Schleimer (Geom Topol 13(3):1495-1497, 2009) discovered a nontrivial root of the Dehn twist about a nonseparating curve on a closed oriented connected surface. McCullough and Rajeevsarathy (Geom Dedicata 151(1):397-409, 2011) and Monden (Rocky Mt J Math, to appear) obtained the evaluation of the degrees of roots of Dehn twists. In this paper, we discuss existence and degrees of homeomorphisms whose power is equal to disk twist about a nonseparating disk in the mapping class group of the 3-dimensional handlebody.",
keywords = "3-Dimensional handlebody, Disk twist, Mapping class group, Root",
author = "Susumu Hirose and Naoyuki Monden",
year = "2013",
month = "6",
day = "1",
doi = "10.1007/s10711-012-9759-4",
language = "English",
volume = "164",
pages = "73--82",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - Degree of roots of disk twists on 3-dimensional handlebodies

AU - Hirose, Susumu

AU - Monden, Naoyuki

PY - 2013/6/1

Y1 - 2013/6/1

N2 - Margalit and Schleimer (Geom Topol 13(3):1495-1497, 2009) discovered a nontrivial root of the Dehn twist about a nonseparating curve on a closed oriented connected surface. McCullough and Rajeevsarathy (Geom Dedicata 151(1):397-409, 2011) and Monden (Rocky Mt J Math, to appear) obtained the evaluation of the degrees of roots of Dehn twists. In this paper, we discuss existence and degrees of homeomorphisms whose power is equal to disk twist about a nonseparating disk in the mapping class group of the 3-dimensional handlebody.

AB - Margalit and Schleimer (Geom Topol 13(3):1495-1497, 2009) discovered a nontrivial root of the Dehn twist about a nonseparating curve on a closed oriented connected surface. McCullough and Rajeevsarathy (Geom Dedicata 151(1):397-409, 2011) and Monden (Rocky Mt J Math, to appear) obtained the evaluation of the degrees of roots of Dehn twists. In this paper, we discuss existence and degrees of homeomorphisms whose power is equal to disk twist about a nonseparating disk in the mapping class group of the 3-dimensional handlebody.

KW - 3-Dimensional handlebody

KW - Disk twist

KW - Mapping class group

KW - Root

UR - http://www.scopus.com/inward/record.url?scp=84877794826&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877794826&partnerID=8YFLogxK

U2 - 10.1007/s10711-012-9759-4

DO - 10.1007/s10711-012-9759-4

M3 - Article

AN - SCOPUS:84877794826

VL - 164

SP - 73

EP - 82

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1

ER -