The Farrell-Jones Conjecture for Hyperbolic-by-Cyclic Groups

被引：3

作者：

Bestvina, Mladen ^{[1
]}

Fujiwara, Koji ^{[2
]}

Wigglesworth, Derrick ^{[3
]}

机构：

[1] Univ Utah, Dept Math, 155 S 1400 E, Salt Lake City, UT 84112 USA

[2] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

[3] Univ Arkansas, Dept Math Sci, 309 SCEN, Fayetteville, AR 72703 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 07期

基金：

美国国家科学基金会;

关键词：

FINITELY PRESENTED GROUPS; AUTOMORPHISMS; SPLITTINGS; RIGIDITY; LATTICES; TREES;

D O I：

10.1093/imrn/rnac012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the Farrell-Jones conjecture (FJC) for mapping tori of automorphisms of virtually torsion-free hyperbolic groups. The proof uses recently developed geometric methods for establishing the FJC by Bartels-Luck-Reich, as well as the structure theory of mapping tori by Dahmani-Krishna.

引用

页码：5887 / 5904

页数：18

共 7 条

[1] The Farrell-Jones Conjecture for mapping class groups
Bartels, Arthur
Bestvina, Mladen
INVENTIONES MATHEMATICAE, 2019, 215 (02) : 651 - 712
[2] Hyperbolic hyperbolic-by-cyclic groups are cubulable
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GEOMETRY & TOPOLOGY, 2025, 29 (01)
[3] Relative hyperbolicity of hyperbolic-by-cyclic groups
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[4] On the Farrell-Jones conjecture for algebraic K-theory of spaces: the Farrell-Hsiang method
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Winges, Christoph
ANNALS OF K-THEORY, 2019, 4 (01) : 57 - 138
[5] THE VISUAL BOUNDARY OF HYPERBOLIC FREE-BY-CYCLIC GROUPS
Algom-Kfir, Yael
Hilion, Arnaud
Stark, Emily
ISRAEL JOURNAL OF MATHEMATICS, 2021, 244 (02) : 501 - 538
[6] CUBULATING HYPERBOLIC FREE-BY-CYCLIC GROUPS: THE IRREDUCIBLE CASE
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Wise, Daniel T.
DUKE MATHEMATICAL JOURNAL, 2016, 165 (09) : 1753 - 1813
[7] Cubulating hyperbolic free-by-cyclic groups: the general case
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Wise, Daniel T.
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2015, 25 (01) : 134 - 179

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