{"title":"半对称拟群同态诱导的分支盖","authors":"Kyle M. Lewis","doi":"10.56415/qrs.v31.06","DOIUrl":null,"url":null,"abstract":"Finite semisymmetric quasigroups are in bijection with certain mappings between abstract polyhedra and directed graphs, termed alignments. We demonstrate the polyhedra of any given alignment can always be realized as compact, orientable surfaces. For any n to N, the class of quasigroups having associated surfaces with sum genus ≤ n is closed under subobjects and homomorphic images. Further, we demonstrate semisymmetric quasigroup homomorphisms may be translated into branched covers between their respective surfaces.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Branched covers induced by semisymmetric quasigroup homomorphisms\",\"authors\":\"Kyle M. Lewis\",\"doi\":\"10.56415/qrs.v31.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Finite semisymmetric quasigroups are in bijection with certain mappings between abstract polyhedra and directed graphs, termed alignments. We demonstrate the polyhedra of any given alignment can always be realized as compact, orientable surfaces. For any n to N, the class of quasigroups having associated surfaces with sum genus ≤ n is closed under subobjects and homomorphic images. Further, we demonstrate semisymmetric quasigroup homomorphisms may be translated into branched covers between their respective surfaces.\",\"PeriodicalId\":38681,\"journal\":{\"name\":\"Quasigroups and Related Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quasigroups and Related Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56415/qrs.v31.06\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v31.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Branched covers induced by semisymmetric quasigroup homomorphisms
Finite semisymmetric quasigroups are in bijection with certain mappings between abstract polyhedra and directed graphs, termed alignments. We demonstrate the polyhedra of any given alignment can always be realized as compact, orientable surfaces. For any n to N, the class of quasigroups having associated surfaces with sum genus ≤ n is closed under subobjects and homomorphic images. Further, we demonstrate semisymmetric quasigroup homomorphisms may be translated into branched covers between their respective surfaces.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
