K3流形束的特征类及Nielsen实现问题

arXiv: Algebraic Topology Pub Date : 2019-07-17 DOI:10.2140/TUNIS.2021.3.75

Jeffrey Giansiracusa, A. Kupers, Bena Tshishiku

{"title":"K3流形束的特征类及Nielsen实现问题","authors":"Jeffrey Giansiracusa, A. Kupers, Bena Tshishiku","doi":"10.2140/TUNIS.2021.3.75","DOIUrl":null,"url":null,"abstract":"Let $K$ be the K3 manifold. In this note, we discuss two methods to prove that certain generalized Miller--Morita--Mumford classes for smooth bundles with fiber $K$ are non-zero. As a consequence, we fill a gap in a paper of the first author, and prove that the homomorphism $Diff(K)\\to \\pi_0 Diff(K)$ does not split. One of the two methods of proof uses a result of Franke on the stable cohomology of arithmetic groups that strengthens work of Borel, and may be of independent interest.","PeriodicalId":8433,"journal":{"name":"arXiv: Algebraic Topology","volume":"94 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem\",\"authors\":\"Jeffrey Giansiracusa, A. Kupers, Bena Tshishiku\",\"doi\":\"10.2140/TUNIS.2021.3.75\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $K$ be the K3 manifold. In this note, we discuss two methods to prove that certain generalized Miller--Morita--Mumford classes for smooth bundles with fiber $K$ are non-zero. As a consequence, we fill a gap in a paper of the first author, and prove that the homomorphism $Diff(K)\\\\to \\\\pi_0 Diff(K)$ does not split. One of the two methods of proof uses a result of Franke on the stable cohomology of arithmetic groups that strengthens work of Borel, and may be of independent interest.\",\"PeriodicalId\":8433,\"journal\":{\"name\":\"arXiv: Algebraic Topology\",\"volume\":\"94 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/TUNIS.2021.3.75\",\"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/10.2140/TUNIS.2021.3.75","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 10

摘要

设K是K3流形。本文讨论了证明具有光纤$K$的光滑束的某些广义Miller—Morita—Mumford类非零的两种方法。因此，我们填补了第一作者论文中的一个空白，并证明了$Diff(K)\到\pi_0 Diff(K)$的同态不分裂。两种证明方法中的一种使用了Franke关于算术群的稳定上同调的结果，该结果加强了Borel的工作，并且可能具有独立的兴趣。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem

Let $K$ be the K3 manifold. In this note, we discuss two methods to prove that certain generalized Miller--Morita--Mumford classes for smooth bundles with fiber $K$ are non-zero. As a consequence, we fill a gap in a paper of the first author, and prove that the homomorphism $Diff(K)\to \pi_0 Diff(K)$ does not split. One of the two methods of proof uses a result of Franke on the stable cohomology of arithmetic groups that strengthens work of Borel, and may be of independent interest.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv: Algebraic Topology

自引率

0.00%

发文量