{"title":"包含 Nil 的投影空间积几何的退化","authors":"Thomas Shifley , Steve Trettel","doi":"10.1016/j.topol.2024.109078","DOIUrl":null,"url":null,"abstract":"<div><div>This paper produces explicit conjugacy paths for the product geometries <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mi>R</mi></math></span> and <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mi>R</mi></math></span> 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 <span><math><mo>(</mo><mrow><mi>PGL</mi></mrow><mo>(</mo><mn>4</mn><mo>,</mo><mi>R</mi><mo>)</mo><mo>,</mo><msup><mrow><mi>RP</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"357 ","pages":"Article 109078"},"PeriodicalIF":0.6000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Degenerations of the product geometries in projective space that contain Nil\",\"authors\":\"Thomas Shifley , Steve Trettel\",\"doi\":\"10.1016/j.topol.2024.109078\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper produces explicit conjugacy paths for the product geometries <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mi>R</mi></math></span> and <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mi>R</mi></math></span> 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 <span><math><mo>(</mo><mrow><mi>PGL</mi></mrow><mo>(</mo><mn>4</mn><mo>,</mo><mi>R</mi><mo>)</mo><mo>,</mo><msup><mrow><mi>RP</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span>.</div></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"357 \",\"pages\":\"Article 109078\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-10-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166864124002633\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864124002633","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Degenerations of the product geometries in projective space that contain Nil
This paper produces explicit conjugacy paths for the product geometries and 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 .
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.