{"title":"词-双曲群的有限可和$\\gamma$-元素","authors":"James M Cabrera, M. Puschnigg","doi":"10.4171/jncg/446","DOIUrl":null,"url":null,"abstract":"We present two explicit combinatorial constructions of finitely summable reduced \"Gamma\"-elements $\\gamma_r\\,\\in\\,KK(C^*_r(\\Gamma),{\\mathbb C})$ for any word-hyperbolic group $(\\Gamma,S)$ and obtain summability bounds for them in terms of the cardinality of the generating set $S\\subset\\Gamma$ and the hyperbolicity constant of the associated Cayley graph.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2020-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finitely summable $\\\\gamma$-elements for word-hyperbolic groups\",\"authors\":\"James M Cabrera, M. Puschnigg\",\"doi\":\"10.4171/jncg/446\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present two explicit combinatorial constructions of finitely summable reduced \\\"Gamma\\\"-elements $\\\\gamma_r\\\\,\\\\in\\\\,KK(C^*_r(\\\\Gamma),{\\\\mathbb C})$ for any word-hyperbolic group $(\\\\Gamma,S)$ and obtain summability bounds for them in terms of the cardinality of the generating set $S\\\\subset\\\\Gamma$ and the hyperbolicity constant of the associated Cayley graph.\",\"PeriodicalId\":54780,\"journal\":{\"name\":\"Journal of Noncommutative Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-01-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Noncommutative Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jncg/446\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Noncommutative Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jncg/446","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Finitely summable $\gamma$-elements for word-hyperbolic groups
We present two explicit combinatorial constructions of finitely summable reduced "Gamma"-elements $\gamma_r\,\in\,KK(C^*_r(\Gamma),{\mathbb C})$ for any word-hyperbolic group $(\Gamma,S)$ and obtain summability bounds for them in terms of the cardinality of the generating set $S\subset\Gamma$ and the hyperbolicity constant of the associated Cayley graph.
期刊介绍：
The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular:
Hochschild and cyclic cohomology
K-theory and index theory
Measure theory and topology of noncommutative spaces, operator algebras
Spectral geometry of noncommutative spaces
Noncommutative algebraic geometry
Hopf algebras and quantum groups
Foliations, groupoids, stacks, gerbes
Deformations and quantization
Noncommutative spaces in number theory and arithmetic geometry
Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.
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