{"title":"Aut(FN) 中自由基的直积","authors":"Martin R. Bridson, Richard D. Wade","doi":"10.1007/s00039-024-00688-5","DOIUrl":null,"url":null,"abstract":"<p>We give a complete description of the embeddings of direct products of nonabelian free groups into Aut(<i>F</i><sub><i>N</i></sub>) and Out(<i>F</i><sub><i>N</i></sub>) when the number of direct factors is maximal. To achieve this, we prove that the image of each such embedding has a canonical fixed point of a particular type in the boundary of Outer space.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Direct Products of Free Groups in Aut(FN)\",\"authors\":\"Martin R. Bridson, Richard D. Wade\",\"doi\":\"10.1007/s00039-024-00688-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give a complete description of the embeddings of direct products of nonabelian free groups into Aut(<i>F</i><sub><i>N</i></sub>) and Out(<i>F</i><sub><i>N</i></sub>) when the number of direct factors is maximal. To achieve this, we prove that the image of each such embedding has a canonical fixed point of a particular type in the boundary of Outer space.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00039-024-00688-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00039-024-00688-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
We give a complete description of the embeddings of direct products of nonabelian free groups into Aut(FN) and Out(FN) when the number of direct factors is maximal. To achieve this, we prove that the image of each such embedding has a canonical fixed point of a particular type in the boundary of Outer space.
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