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

[21] FRATTINI SUBGROUPS OF 3-MANIFOLD GROUPS
ALLENBY, RBJT
BOLER, J
EVANS, B
MOSER, LE
TANG, CY
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 247 (JAN) : 275 - 300
[22] SUBGROUP SEPARABILITY AND 3-MANIFOLD GROUPS
LONG, DD
NIBLO, GA
MATHEMATISCHE ZEITSCHRIFT, 1991, 207 (02) : 209 - 215
[23] On representation varieties of 3-manifold groups
Kapovich, Michael
Millson, John J.
GEOMETRY & TOPOLOGY, 2017, 21 (04) : 1931 - 1968
[24] SUBGROUP DISTORTION OF 3-MANIFOLD GROUPS
Hoang Thanh Nguyen
Sun, Hongbin
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 373 (09) : 6683 - 6711
[25] SUBNORMAL SUBGROUPS IN 3-MANIFOLD GROUPS
ELKALLA, HS
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1984, 30 (OCT): : 342 - 360
[26] 3-manifold Groups and Nonpositive Curvature
M. Kapovich
B. Leeb
Geometric & Functional Analysis GAFA, 1998, 8 : 841 - 852
[27] Free subgroups of 3-manifold groups
Belolipetsky, Mikhail
Doria, Cayo
GROUPS GEOMETRY AND DYNAMICS, 2020, 14 (01) : 243 - 254
[28] A NOTE ON CENTRALITY IN 3-MANIFOLD GROUPS
KROPHOLLER, PH
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1990, 107 : 261 - 266
[29] 3-MANIFOLD GROUPS, KAHLER GROUPS AND COMPLEX SURFACES
Biswas, Indranil
Mj, Mahan
Seshadri, Harish
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2012, 14 (06)
[30] Virtually cyclic dimension for 3-manifold groups
Joecken, Kyle
Lafont, Jean-Francois
Sanchez Saldana, Luis Jorge
GROUPS GEOMETRY AND DYNAMICS, 2021, 15 (02) : 577 - 606

← 1 2 3 4 5 →