论文标题
奇数流形的差异性的一些合理同源计算
Some rational homology computations for diffeomorphisms of odd-dimensional manifolds
论文作者
论文摘要
We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}{D^{2n+1}}$, for large $g$ and $n$, up to approximately degree $n$.答案是，它是一组适当的米勒 - 穆里塔 - 穆福德课程的免费分级的交换代数。 我们的证明是经典的三步程序：（a）计算同型自动形态的共同体学，（b）使用手术来比较这一点来阻止差异性，（c）使用伪异吞理论和代数$ k $ - 在实际的差异群中获得实际的差异群体。
We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}{D^{2n+1}}$, for large $g$ and $n$, up to approximately degree $n$. 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, (c) use pseudoisotopy theory and algebraic $K$-theory to get at actual diffeomorphism groups.
