EPIMORPHISMS OF 3-MANIFOLD GROUPS

被引：0

作者：

Boileau, Michel ^{[1
]}

Friedl, Stefan ^{[2
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M, Marseille, France

[2] Univ Regensburg, Fak Math, Regensburg, Germany

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2018年 / 69卷 / 03期

关键词：

GRAPH MANIFOLDS; HEEGAARD-SPLITTINGS; HAKEN CONJECTURE; SURFACE BUNDLES; CYCLIC COVERS; RANK; RIGIDITY; GENUS;

D O I：

10.1093/qmath/hay007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f: M -> N be a proper map between two aspherical compact orientable 3-manifolds with empty or toroidal boundary. We assume that N is not a closed graph manifold. Suppose that f induces an epimorphism on fundamental groups. We show that f is homotopic to a homeomorphism if one of the following holds: either for any finite-index subgroup Gamma of pi(1)(N) the ranks of Gamma and of f(*)(-1) (Gamma) agree, or for any finite cover (N) over tilde of N the Heegaard genus of (N) over tilde and the Heegaard genus of the pull-back cover (M) over tilde agree.

引用

页码：931 / 942

页数：12

共 50 条

[1] Generalized hopfian property, a minimal Haken manifold, and epimorphisms between 3-manifold groups
Reid, AW
Wang, SC
Zhou, Q
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2002, 18 (01) : 157 - 172
[2] Generalized Hopfian Property, a Minimal Haken Manifold, and Epimorphisms Between 3-Manifold Groups
Alan W. Reid
Shi Cheng Wang
Qing Zhou
Acta Mathematica Sinica, 2002, 18 : 157 - 172
[3] Generalized Hopfian Property, a Minimal Haken Manifold, and Epimorphisms Between 3-Manifold Groups
REID Alan W
ActaMathematicaSinica(EnglishSeries), 2002, 18 (01) : 157 - 172
[4] COHOPFICITY OF 3-MANIFOLD GROUPS
GONZALEZACUNA, F
WHITTEN, W
TOPOLOGY AND ITS APPLICATIONS, 1994, 56 (01) : 87 - 97
[5] DIVERGENCE IN 3-MANIFOLD GROUPS
GERSTEN, SM
GEOMETRIC AND FUNCTIONAL ANALYSIS, 1994, 4 (06) : 633 - 647
[6] Orderable 3-manifold groups
Boyer, S
Rolfsen, D
Wiest, B
ANNALES DE L INSTITUT FOURIER, 2005, 55 (01) : 243 - +
[7] 3-MANIFOLD GROUPS - SURVEY
JACO, W
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (07): : A732 - A733
[8] IMBEDDINGS OF 3-MANIFOLD GROUPS
GONZALEZACUNA, F
WHITTEN, WC
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 99 (474) : 1 - 55
[9] Quasiconvexity in 3-manifold groups
Hoang Thanh Nguyen
Hung Cong Tran
Wenyuan Yang
Mathematische Annalen, 2021, 381 : 405 - 437
[10] Quasiconvexity in 3-manifold groups
Hoang Thanh Nguyen
Hung Cong Tran
Yang, Wenyuan
MATHEMATISCHE ANNALEN, 2020, 381 (1-2) : 405 - 437

← 1 2 3 4 5 →