Degree of roots of disk twists on 3-dimensional handlebodies

Susumu Hirose; Naoyuki Monden

doi:10.1007/s10711-012-9759-4

Degree of roots of disk twists on 3-dimensional handlebodies

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

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 language	English
Pages (from-to)	73-82
Number of pages	10
Journal	Geometriae Dedicata
Volume	164
Issue number	1
DOIs	https://doi.org/10.1007/s10711-012-9759-4
Publication status	Published - Jun 2013
Externally published	Yes

Keywords

3-Dimensional handlebody
Disk twist
Mapping class group
Root

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s10711-012-9759-4

Cite this

@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",

note = "Funding Information: Acknowledgments The first author was supported by Grant-in-Aid for Scientific Research (C) (No. 24540096), Japan Society for the Promotion of Science. The authors thank to Professor Yuya Koda for inspiring us to think about this problem.",

year = "2013",

month = jun,

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

N1 - Funding Information: Acknowledgments The first author was supported by Grant-in-Aid for Scientific Research (C) (No. 24540096), Japan Society for the Promotion of Science. The authors thank to Professor Yuya Koda for inspiring us to think about this problem.

PY - 2013/6

Y1 - 2013/6

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

SN - 0046-5755

VL - 164

SP - 73

EP - 82

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Degree of roots of disk twists on 3-dimensional handlebodies

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this