{"title":"无穷零曼形上仿 n 值映射的尼尔森数平均公式","authors":"Karel Dekimpe, Lore De Weerdt","doi":"10.1007/s00574-024-00417-4","DOIUrl":null,"url":null,"abstract":"<p>In Kim et al. (Nagoya Math J 178: 37-53, 2005), Lee and Lee (J Geometry Phys 56(10): 2011-2023, 2006), the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to <i>n</i>-valued maps in Deconinck and Dekimpe (J Fixed Point Theory Appl 25(4): Paper No. 84, 29, 2023). In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any <i>n</i>-valued affine map on an infra-nilmanifold.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Averaging Formula for Nielsen Numbers of Affine n-Valued Maps on Infra-Nilmanifolds\",\"authors\":\"Karel Dekimpe, Lore De Weerdt\",\"doi\":\"10.1007/s00574-024-00417-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In Kim et al. (Nagoya Math J 178: 37-53, 2005), Lee and Lee (J Geometry Phys 56(10): 2011-2023, 2006), the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to <i>n</i>-valued maps in Deconinck and Dekimpe (J Fixed Point Theory Appl 25(4): Paper No. 84, 29, 2023). In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any <i>n</i>-valued affine map on an infra-nilmanifold.</p>\",\"PeriodicalId\":501417,\"journal\":{\"name\":\"Bulletin of the Brazilian Mathematical Society, New Series\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Brazilian Mathematical Society, New Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00574-024-00417-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Brazilian Mathematical Society, New Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00574-024-00417-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在 Kim 等人 (Nagoya Math J 178: 37-53, 2005), Lee 和 Lee (J Geometry Phys 56(10)：2011-2023，2006）中，作者们提出了一个计算下零曼形上自映射的尼尔森数的漂亮公式。德科宁克和德金佩在《定点理论应用》（J Fixed Point Theory Appl 25(4)：论文编号 84, 29, 2023）。在本文中，我们进一步扩展了这些结果，并建立了平均公式来计算下无穷面上任何 n 值仿射映射的尼尔森数。
An Averaging Formula for Nielsen Numbers of Affine n-Valued Maps on Infra-Nilmanifolds
In Kim et al. (Nagoya Math J 178: 37-53, 2005), Lee and Lee (J Geometry Phys 56(10): 2011-2023, 2006), the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to n-valued maps in Deconinck and Dekimpe (J Fixed Point Theory Appl 25(4): Paper No. 84, 29, 2023). In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any n-valued affine map on an infra-nilmanifold.
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