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

Wei Wang

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arXiv · 2504.04875

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

Wei Wang

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Abstract

In this paper, we compute some Gromoll filtration groups $\Gamma^{n+1}_{i+1}$ for certain $i$ when $8\leq n \leq 17$ and $n=4k+2\geq 18$. Using these results, we obtain some new information on $\pi_1\mathrm{Diff}_{\partial} (D^n)$ for $6\leq n \leq 15$ and on $\pi_2 \mathrm{Diff}_{\partial} (D^{4k+3})$ for $4k+3\geq 15$.

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Wei Wang. 2025-04-07. On some Gromoll filtration groups and fundamental groups of $\mathrm{Diff}_{\partial}(D^n)$. https://arxiv.org/abs/2504.04875

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