On a generalization of Cannon's conjecture for cubulated hyperbolic groups.

IF 1.8 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2026-01-01 Epub Date: 2026-09-24 DOI:10.1007/s00208-026-03529-y

Corey Bregman, Merlin Incerti-Medici

引用次数: 0

Abstract

We show that cubulated hyperbolic groups with spherical boundary of dimension 3 or at least 5 are virtually fundamental groups of closed, orientable, aspherical manifolds, provided that there are sufficiently many quasi-convex, codimension-1 subgroups whose limit sets are locally flat subspheres. The proof is based on ideas used by Markovic in his work on Cannon's conjecture for cubulated hyperbolic groups with 2-sphere boundary.

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关于计算双曲群的Cannon猜想的推广。

我们证明了球面边界为3维或至少5维的曲型双曲群是闭的、可定向的、非球面流形的基本群，只要有足够多的准凸的、余维为1的子群，其极限集是局部平的子球。这个证明是基于Markovic在他关于2球边界的计算双曲群的Cannon猜想的工作中使用的思想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.