A finite-dimensional approach to the strong Novikov conjecture
A finite-dimensional approach to the strong Novikov conjecture
复制标题
强诺维科夫猜想的有限维方法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Guoliang Yu
中科院分区：
文献类型：
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作者：
D. Ramras;R. Willett;Guoliang Yu
本文的目的是描述一种基于有限维连续表示族的(强)Novikov猜想的方法：这部分是受到Lusztig关于Atiyah-Singer族指标定理的思想的启发，部分是受到Carlsson变形K-理论的启发。利用这种方法，我们在几种有趣的情况下，包括晶体群和表面群，给出了强Novikov猜想的新证明。与Novikov猜想的其他证明相比，本文给出的方法是相对可行的，并给出了关于表示空间的K-理论和上同调的一些信息。19K56、19L99、55N15、57R20；20C99、46L80、46L85
The aim of this paper is to describe an approach to the (strong) Novikov conjecture based on continuous families of finite-dimensional representations: this is partly inspired by ideas of Lusztig related to the Atiyah‐Singer families index theorem, and partly by Carlsson’s deformation K‐theory. Using this approach, we give new proofs of the strong Novikov conjecture in several interesting cases, including crystallographic groups and surface groups. The method presented here is relatively accessible compared with other proofs of the Novikov conjecture, and also yields some information about the K‐theory and cohomology of representation spaces. 19K56, 19L99, 55N15, 57R20; 20C99, 46L80, 46L85