{"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}
引用次数: 0
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.