Failure of separation by quasi-homomorphisms in mapping class groups

被引：2

作者：

Endo, H. ^{[1
]}

Kotschick, D.

机构：

[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

[2] Univ Munich, Inst Math, D-80333 Munich, Germany

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 135卷 / 09期

关键词：

D O I：

10.1090/S0002-9939-07-08866-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that mapping class groups of surfaces of genus at least two contain elements of infinite order that are not conjugate to their inverses, but whose powers have bounded torsion lengths. In particular every homogeneous quasi-homomorphism vanishes on such an element, showing that elements of infinite order not conjugate to their inverses cannot be separated by quasi-homomorphisms.

引用

页码：2747 / 2750

页数：4

共 50 条

[41] From braid groups to mapping class groups
Lei Chen
Aru Mukherjea
Mathematische Zeitschrift, 2023, 303
[42] Generalized braid groups and mapping class groups
Labruere, C
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1996, 322 (08): : 753 - 756
[43] Hyperelliptic curves and homomorphisms to ideal class groups of quadratic number fields
Sivertsen, Tormod Kalberg
Soleng, Ragnar
JOURNAL OF NUMBER THEORY, 2011, 131 (12) : 2303 - 2309
[44] Extending Johnson's and Morita's homomorphisms to the mapping class group
Day, Matthew B.
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2007, 7 : 1297 - 1326
[45] From mapping class groups to automorphism groups of free groups
Wahl, N
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2005, 72 : 510 - 524
[46] Brunnian subgroups of mapping class groups and braid groups
Berrick, A. J.
Hanbury, E.
Wu, J.
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2013, 107 : 875 - 906
[47] On the homology of big mapping class groups
Palmer, Martin
Wu, Xiaolei
JOURNAL OF TOPOLOGY, 2024, 17 (04)
[48] Random walks on mapping class groups
Baik, Hyungryul
Choi, Inhyeok
EMS SURVEYS IN MATHEMATICAL SCIENCES, 2022, 9 (02) : 279 - 320
[49] TWO QUESTIONS ON MAPPING CLASS GROUPS
Funar, Louis
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139 (01) : 375 - 382
[50] Dimension and rank for mapping class groups
Behrstock, Jason A.
Minsky, Yair N.
ANNALS OF MATHEMATICS, 2008, 167 (03) : 1055 - 1077

← 1 2 3 4 5 →