{"title":"具有层次结构的拓扑模形式:分解与对偶","authors":"Lennart Meier","doi":"10.1090/tran/8514","DOIUrl":null,"url":null,"abstract":"Topological modular forms with level structure were introduced in full generality by Hill and Lawson. We will show that these decompose additively in many cases into a few simple pieces and give an application to equivariant $TMF$. Furthermore, we show which $Tmf_1(n)$ are self-Anderson dual up to a shift, both with and without their natural $C_2$-action.","PeriodicalId":8433,"journal":{"name":"arXiv: Algebraic Topology","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":"{\"title\":\"Topological modular forms with level structure: Decompositions and duality\",\"authors\":\"Lennart Meier\",\"doi\":\"10.1090/tran/8514\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Topological modular forms with level structure were introduced in full generality by Hill and Lawson. We will show that these decompose additively in many cases into a few simple pieces and give an application to equivariant $TMF$. Furthermore, we show which $Tmf_1(n)$ are self-Anderson dual up to a shift, both with and without their natural $C_2$-action.\",\"PeriodicalId\":8433,\"journal\":{\"name\":\"arXiv: Algebraic Topology\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-06-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/tran/8514\",\"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: Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tran/8514","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Topological modular forms with level structure: Decompositions and duality
Topological modular forms with level structure were introduced in full generality by Hill and Lawson. We will show that these decompose additively in many cases into a few simple pieces and give an application to equivariant $TMF$. Furthermore, we show which $Tmf_1(n)$ are self-Anderson dual up to a shift, both with and without their natural $C_2$-action.
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