{"title":"透镜空间，可作为平面上同调协的闭包实现","authors":"Nozomu Sekino","doi":"10.1215/00192082-8642515","DOIUrl":null,"url":null,"abstract":"We determine the condition on a given lens space having a realization as a closure of homology cobordism over a planar surface with a given number of boundary components. As a corollary, we see that every lens space is represented as a closure of homology cobordism over a planar surface with three boundary components. In the proof of this corollary, we use Chebotarev density theorem.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"5 4","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Lens spaces which are realizable as closures of homology cobordisms over planar surfaces\",\"authors\":\"Nozomu Sekino\",\"doi\":\"10.1215/00192082-8642515\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We determine the condition on a given lens space having a realization as a closure of homology cobordism over a planar surface with a given number of boundary components. As a corollary, we see that every lens space is represented as a closure of homology cobordism over a planar surface with three boundary components. In the proof of this corollary, we use Chebotarev density theorem.\",\"PeriodicalId\":8454,\"journal\":{\"name\":\"arXiv: Geometric Topology\",\"volume\":\"5 4\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1215/00192082-8642515\",\"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/10.1215/00192082-8642515","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lens spaces which are realizable as closures of homology cobordisms over planar surfaces
We determine the condition on a given lens space having a realization as a closure of homology cobordism over a planar surface with a given number of boundary components. As a corollary, we see that every lens space is represented as a closure of homology cobordism over a planar surface with three boundary components. In the proof of this corollary, we use Chebotarev density theorem.
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