{"title":"亚历山大·戈尔德球和冰分解","authors":"Stefan Behrens, Min Hoon Kim","doi":"10.1093/oso/9780198841319.003.0005","DOIUrl":null,"url":null,"abstract":"‘The Alexander Gored Ball and the Bing Decomposition’ provides a concrete and nontrivial application of the tools of decomposition space theory introduced in the previous chapter. The complement of the Alexander horned ball in the 3-sphere is called the Alexander gored ball. This space is described in three distinct ways: as an intersection of 3-balls; as a 3-dimensional grope; and as a decomposition space. Bing’s theorem that the double of the Alexander gored ball is homeomorphic to the 3-sphere is presented. This gives the first example of a truly nontrivial shrink and, moreover, an example of an exotic involution of the 3-sphere.","PeriodicalId":272723,"journal":{"name":"The Disc Embedding Theorem","volume":"39 2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Alexander Gored Ball and the Bing Decomposition\",\"authors\":\"Stefan Behrens, Min Hoon Kim\",\"doi\":\"10.1093/oso/9780198841319.003.0005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"‘The Alexander Gored Ball and the Bing Decomposition’ provides a concrete and nontrivial application of the tools of decomposition space theory introduced in the previous chapter. The complement of the Alexander horned ball in the 3-sphere is called the Alexander gored ball. This space is described in three distinct ways: as an intersection of 3-balls; as a 3-dimensional grope; and as a decomposition space. Bing’s theorem that the double of the Alexander gored ball is homeomorphic to the 3-sphere is presented. This gives the first example of a truly nontrivial shrink and, moreover, an example of an exotic involution of the 3-sphere.\",\"PeriodicalId\":272723,\"journal\":{\"name\":\"The Disc Embedding Theorem\",\"volume\":\"39 2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Disc Embedding Theorem\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/oso/9780198841319.003.0005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Disc Embedding Theorem","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/oso/9780198841319.003.0005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Alexander Gored Ball and the Bing Decomposition
‘The Alexander Gored Ball and the Bing Decomposition’ provides a concrete and nontrivial application of the tools of decomposition space theory introduced in the previous chapter. The complement of the Alexander horned ball in the 3-sphere is called the Alexander gored ball. This space is described in three distinct ways: as an intersection of 3-balls; as a 3-dimensional grope; and as a decomposition space. Bing’s theorem that the double of the Alexander gored ball is homeomorphic to the 3-sphere is presented. This gives the first example of a truly nontrivial shrink and, moreover, an example of an exotic involution of the 3-sphere.