Scholarlink

<p>This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {Z}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Z</mi> </math></EquationSource> </InlineEquation> that is flexible enough to yield infinitely many isomorphism classes in each virtual cohomological dimension (vcd) <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. Our procedure combines results of Jankiewicz, Norin, and Wise with a generalization of a construction due to Osajda involving a new simplicial thickening process. We also give a topological argument showing that the vcd of the right-angled Coxeter groups produced by our construction increases by exactly one with each iteration, guaranteeing that our process produces examples of every vcd.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

High dimensional hyperbolic Coxeter groups that virtually fiber

  • 期刊论文

  • 发表日期：

    2025年9月30日

查看全文
  • Jean-François Lafont,
  • Barry Minemyer,
  • Gangotryi Sorcar,
  • Matthew Stover,
  • Joseph Wells

摘要

This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over \(\mathbb {Z}\) Z that is flexible enough to yield infinitely many isomorphism classes in each virtual cohomological dimension (vcd) \(n\ge 2\) n ≥ 2 . Our procedure combines results of Jankiewicz, Norin, and Wise with a generalization of a construction due to Osajda involving a new simplicial thickening process. We also give a topological argument showing that the vcd of the right-angled Coxeter groups produced by our construction increases by exactly one with each iteration, guaranteeing that our process produces examples of every vcd.