On some Gromoll filtration groups and fundamental groups of ${\mathrm{Diff}}_{\partial }(D^n)$

Abstract

In this paper, we compute some Gromoll filtration groups ${\Gamma }_{i+1}^{n+1}$ for certain $i$ when $8\le n\le 17$ and $n=4k+2\ge 18$. Using these results, we obtain some new information on ${\pi }_1{\mathrm{Diff}}_{\partial }(D^n)$ for $6\le n\le 15$ and on ${\pi }_2{\mathrm{Diff}}_{\partial }(D^{4k+3})$ for $4k+3\ge 15$.

v2: This version revises the title, main theorem statements, general text content, and minor typos. To appear in Math. Z