THE L2-TORSION POLYTOPE OF AMENABLE GROUPS

被引：0

作者：

Funke, Florian ^{[1
]}

机构：

[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

DOCUMENTA MATHEMATICA | 2018年 / 23卷

关键词：

L-2-torsion polytope; amenable groups; polytope class; Atiyah Conjecture; 3-manifolds; L-2-ALEXANDER TORSION; THEOREM; FINITE;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the notion of groups of polytope class and show that torsion-free amenable groups satisfying the Atiyah Conjecture possess this property. A direct consequence is the homotopy invariance of the L-2-torsion polytope among G-CW-complexes for these groups. As another application we prove that the L-2-torsion polytope of an amenable group vanishes provided that it contains a non-abelian elementary amenable normal subgroup.

引用

页码：1969 / 1993

页数：25

共 50 条

[21] Constructions of torsion-free countable, amenable, weakly mixing groups
Grigorchuk, Rostislav
Kravchenko, Rostyslav
Olshanskii, Alexander
ENSEIGNEMENT MATHEMATIQUE, 2015, 61 (3-4): : 321 - 342
[22] TORSION IN L-GROUPS
CAPPELL, SE
SHANESON, JL
LECTURE NOTES IN MATHEMATICS, 1985, 1126 : 22 - 50
[23] AMENABLE TRANSFORMATION GROUPS .2.
SAKAI, K
PROCEEDINGS OF THE JAPAN ACADEMY, 1973, 49 (06): : 428 - 431
[24] On the L p -distortion of finite quotients of amenable groups
Tessera, Romain
POSITIVITY, 2012, 16 (04) : 633 - 640
[25] AMENABLE-GROUPS AND AMENABLE GRAPHS
GERL, P
LECTURE NOTES IN MATHEMATICS, 1988, 1359 : 181 - 190
[26] AMENABLE GROUPS AND VARIETIES OF GROUPS
KELLER, G
ILLINOIS JOURNAL OF MATHEMATICS, 1972, 16 (02) : 257 - &
[27] TORSION THEORY FOR LATTICE-ORDERED GROUPS .2. HOMOGENEOUS L-GROUPS
MARTINEZ, J
CZECHOSLOVAK MATHEMATICAL JOURNAL, 1976, 26 (01) : 93 - 100
[28] Lattices in amenable groups
Bader, Uri
Caprace, Pierre-Emmanuel
Gelander, Tsachik
Mozes, Shahar
FUNDAMENTA MATHEMATICAE, 2019, 246 (03) : 217 - 255
[29] SUBSEMIGROUPS OF AMENABLE GROUPS
HOCHSTER, M
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 21 (02) : 363 - &
[30] Amenable hyperbolic groups
Caprace, Pierre-Emmanuel
Cornulier, Yves
Monod, Nicolas
Tessera, Romain
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2015, 17 (11) : 2903 - 2947

← 1 2 3 4 5 →