Degenerations of the product geometries in projective space that contain Nil

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-10-15 DOI:10.1016/j.topol.2024.109078

Thomas Shifley , Steve Trettel

引用次数: 0

Abstract

This paper produces explicit conjugacy paths for the product geometries

H^{2} \times R

and

S^{2} \times R

whose limits contain the geometry of the Heisenberg group's action on itself. These are the first such conjugacy limits to any model of Nil, continuing the program of Daryl Cooper, Jeffrey Danciger, and Anna Wienhard to determine all possible degenerations between Thurston geometries in

(PGL (4, R), {RP}^{3})

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包含 Nil 的投影空间积几何的退化

本文为乘积几何 H2×R 和 S2×R 提出了明确的共轭路径，其极限包含海森堡群作用于自身的几何。这是任何 Nil 模型的第一个此类共轭极限，延续了 Daryl Cooper、Jeffrey Danciger 和 Anna Wienhard 的计划，即确定 (PGL(4,R),RP3) 中 Thurston 几何图形之间所有可能的退化。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.