{"title":"具有有限基群的4-流形的2-稳定分类","authors":"Daniel Kasprowski, P. Teichner","doi":"10.2140/PJM.2021.310.355","DOIUrl":null,"url":null,"abstract":"We show that two closed, connected $4$-manifolds with finite fundamental groups are $\\mathbb{CP}^2$-stably homeomorphic if and only if their quadratic $2$-types are stably isomorphic and their Kirby-Siebenmann invariant agrees.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"67 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"ℂℙ2-stable classification of 4-manifolds with\\nfinite fundamental group\",\"authors\":\"Daniel Kasprowski, P. Teichner\",\"doi\":\"10.2140/PJM.2021.310.355\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that two closed, connected $4$-manifolds with finite fundamental groups are $\\\\mathbb{CP}^2$-stably homeomorphic if and only if their quadratic $2$-types are stably isomorphic and their Kirby-Siebenmann invariant agrees.\",\"PeriodicalId\":8454,\"journal\":{\"name\":\"arXiv: Geometric Topology\",\"volume\":\"67 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/PJM.2021.310.355\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/PJM.2021.310.355","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ℂℙ2-stable classification of 4-manifolds with
finite fundamental group
We show that two closed, connected $4$-manifolds with finite fundamental groups are $\mathbb{CP}^2$-stably homeomorphic if and only if their quadratic $2$-types are stably isomorphic and their Kirby-Siebenmann invariant agrees.
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