论文标题
伪异吞理论的同源方法。我
A homological approach to pseudoisotopy theory. I
论文作者
论文摘要
我们从曾经封闭的$ 2N $ -DISC的伪异型的空间中构造了一个曲折ZAG，到曾经循环的代数$ k $ - 整数的理论空间，并表明所涉及的地图是$ p $ - loclocally $（2n-4）$ - 连接了$ n> 3 $ n> 3 $ n> 3 $ and ligh Primes $ prime $ p $ P $ $ P。该证明使用了由于botvinnik-perlmutter引起的高维操纵箱模量空间的稳定同源性的计算，并且独立于基于Igusa的稳定性理论和Waldhausen的工作的古典方法。结合Randal-Williams的结果，此识别的结果是计算$ \ Mathrm {bdiff} _ \ partial（d^{2n+1}）$的理性同拷贝组，最高$ 2n-5 $。
We construct a zig-zag from the once delooped space of pseudoisotopies of a closed $2n$-disc to the once looped algebraic $K$-theory space of the integers and show that the maps involved are $p$-locally $(2n-4)$-connected for $n>3$ and large primes $p$. The proof uses the computation of the stable homology of the moduli space of high-dimensional handlebodies due to Botvinnik--Perlmutter and is independent of the classical approach to pseudoisotopy theory based on Igusa's stability theorem and work of Waldhausen. Combined with a result of Randal-Williams, one consequence of this identification is a calculation of the rational homotopy groups of $\mathrm{BDiff}_\partial(D^{2n+1})$ in degrees up to $2n-5$.
