English

A short note on $\pi_1\mathrm{Diff}_{\partial} (D^{4k})$ for $k\geq 3$

Algebraic Topology 2024-04-12 v2 Geometric Topology

Abstract

Let Diff(Dn)\mathrm{Diff}_{\partial}(D^{n}) be the topological group of diffeomorphisms of DnD^{n} which agree with the identity near the boundary. In this short note, we compute the fundamental groups π1Diff(D4k)\pi_1 \mathrm{Diff}_{\partial}(D^{4k}) for k3k\geq 3.

Cite

@article{arxiv.2307.03417,
  title  = {A short note on $\pi_1\mathrm{Diff}_{\partial} (D^{4k})$ for $k\geq 3$},
  author = {Wei Wang},
  journal= {arXiv preprint arXiv:2307.03417},
  year   = {2024}
}

Comments

7 Pages. Some improvements and corrections based on two anonymous referees' reports. Final version, to appear in Proc. AMS

R2 v1 2026-06-28T11:24:19.084Z