{"title":"球面积的连通和的自等价稳定同调","authors":"Robin Stoll","doi":"10.1017/fms.2023.113","DOIUrl":null,"url":null,"abstract":"<p>We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240105121641127-0961:S2050509423001135:S2050509423001135_inline1.png\"><span data-mathjax-type=\"texmath\"><span>${\\mathrm {S}^{k}} \\times {\\mathrm {S}^{l}}$</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240105121641127-0961:S2050509423001135:S2050509423001135_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$3 \\le k < l \\le 2k - 2$</span></span></img></span></span>. The result is expressed in terms of Lie graph complex homology.</p>","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The stable cohomology of self-equivalences of connected sums of products of spheres\",\"authors\":\"Robin Stoll\",\"doi\":\"10.1017/fms.2023.113\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240105121641127-0961:S2050509423001135:S2050509423001135_inline1.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>${\\\\mathrm {S}^{k}} \\\\times {\\\\mathrm {S}^{l}}$</span></span></img></span></span>, where <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240105121641127-0961:S2050509423001135:S2050509423001135_inline2.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$3 \\\\le k < l \\\\le 2k - 2$</span></span></img></span></span>. The result is expressed in terms of Lie graph complex homology.</p>\",\"PeriodicalId\":56000,\"journal\":{\"name\":\"Forum of Mathematics Sigma\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Forum of Mathematics Sigma\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/fms.2023.113\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Forum of Mathematics Sigma","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/fms.2023.113","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们确定了 ${mathrm {S}^{k}} 的连接和的同调自变量（相对于嵌入盘）的稳定分类空间的同调。\times {\mathrm {S}^{l}}$, where $3 \le k < l \le 2k - 2$.这个结果用李图复同调来表示。
The stable cohomology of self-equivalences of connected sums of products of spheres
We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of ${\mathrm {S}^{k}} \times {\mathrm {S}^{l}}$, where $3 \le k < l \le 2k - 2$. The result is expressed in terms of Lie graph complex homology.
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${\mathrm {S}^{k}} \times {\mathrm {S}^{l}}$, where 
$3 \le k < l \le 2k - 2$. The result is expressed in terms of Lie graph complex homology.
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