论文标题
通过$ e_k $ -algebras的高维流形的差异群的同构稳定性
Homological stability of diffeomorphism groups of high dimensional manifolds via $E_k$-algebras
论文作者
论文摘要
我们将研究歧管的差异组的同源稳定性$ w_ {g，1}：= d^{2n} \＃（s^n \ times s^n）^{\＃g} $使用$ e_k $ -algebras。这将导致稳定结果的新改善，尤其是在使用合理系数时。此外，我们将证明一种新型的稳定性结果 - 量化的同源稳定性 - 说最佳稳定性结果是斜率$ 1/2 $的线性界限，或者稳定性至少与斜率$ 2/3 $的线一样好。
We will study homological stability of the diffeomorphism groups of the manifolds $W_{g,1}:=D^{2n} \# (S^n \times S^n)^{\#g }$ using $E_k$-algebras. This will lead to new improvements in the stability results, especially when working with rational coefficients. Moreover, we will prove a new type of stability result -- quantised homological stability -- which says that either the best stability result is a linear bound of slope $1/2$ or the stability is at least as good as a line of slope $2/3$.
