{"title":"体积熵半范数和收缩体积半范数","authors":"I. Babenko, S. Sabourau","doi":"10.4171/jems/1370","DOIUrl":null,"url":null,"abstract":"We introduce the volume entropy semi-norm and the systolic volume semi-norm in real homology and show that they satisfy functorial properties similar to the ones of the simplicial volume. Along the way, we also establish a roughly optimal upper bound on the systolic volume of the multiples of any homology class. Finally, we prove that the volume entropy semi-norm, the systolic volume semi-norm and the simplicial volume semi-norm are equivalent in every dimension.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Volume entropy semi-norm and systolic volume semi-norm\",\"authors\":\"I. Babenko, S. Sabourau\",\"doi\":\"10.4171/jems/1370\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the volume entropy semi-norm and the systolic volume semi-norm in real homology and show that they satisfy functorial properties similar to the ones of the simplicial volume. Along the way, we also establish a roughly optimal upper bound on the systolic volume of the multiples of any homology class. Finally, we prove that the volume entropy semi-norm, the systolic volume semi-norm and the simplicial volume semi-norm are equivalent in every dimension.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2023-08-03\",\"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/10.4171/jems/1370\",\"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/10.4171/jems/1370","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Volume entropy semi-norm and systolic volume semi-norm
We introduce the volume entropy semi-norm and the systolic volume semi-norm in real homology and show that they satisfy functorial properties similar to the ones of the simplicial volume. Along the way, we also establish a roughly optimal upper bound on the systolic volume of the multiples of any homology class. Finally, we prove that the volume entropy semi-norm, the systolic volume semi-norm and the simplicial volume semi-norm are equivalent in every dimension.
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