当前位置: X-MOL 学术J. Topol. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Some rational homology computations for diffeomorphisms of odd-dimensional manifolds
Journal of Topology ( IF 0.8 ) Pub Date : 2024-01-31 , DOI: 10.1112/topo.12324
Johannes Ebert 1 , Jens Reinhold 1
Affiliation  

We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds U g , 1 n : = # g ( S n × S n + 1 ) int ( D 2 n + 1 ) $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}(D^{2n+1})$ , for large g $g$ and n $n$ , up to degree n 3 $n-3$ . The answer is that it is a free graded commutative algebra on an appropriate set of Miller–Morita–Mumford classes. Our proof goes through the classical three-step procedure: (a) compute the cohomology of the homotopy automorphisms, (b) use surgery to compare this to block diffeomorphisms, and (c) use pseudoisotopy theory and algebraic K $K$ -theory to get at actual diffeomorphism groups.

中文翻译:

奇维流形微分同胚的一些有理同调计算

我们计算流形微分同胚群分类空间的有理上同调 U G , 1 n : = # G S n × S n + 1 整数 D 2 n + 1 $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}(D^{2n+1})$ ,对于大 G $g$ n $n$ , 达到程度 n - 3 $n-3$ 。答案是,它是一组适当的 Miller-Morita-Mumford 类上的自由分级交换代数。我们的证明经历了经典的三步过程:(a)计算同伦自同构的上同调,(b)使用手术将其与块微分同胚进行比较,以及(c)使用伪同位素理论和代数 K $K$ -获得实际微分同胚群的理论。
更新日期:2024-02-04
down
wechat
bug