A short note on 𝜋₁(𝐷𝑖𝑓𝑓_{∂}𝐷^{4𝑘}) for 𝑘≥3

Pub Date : 2024-05-11 DOI:10.1090/proc/16908

Wei Wang

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Abstract

Let Diff ∂ ⁡ ( D n ) \operatorname {Diff}_{\partial }(D^{n}) be the topological group of diffeomorphisms of D n D^{n} which agree with the identity near the boundary. In this short note, we compute the fundamental group π 1 Diff ∂ ⁡ ( D 4 k ) \pi _1 \operatorname {Diff}_{\partial }(D^{4k}) for k ≥ 3 k\geq 3 .

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关于𝜋₁(𝐷𝑖𝑓𝑓_{∂}𝐷^{4𝑘})的简短说明，适用于 𝑘≥3

让 Diff ∂ ( D n ) （operatorname {Diff}_{\partial }(D^{n}）是 D n D^{n} 的差分变形的拓扑群，它与边界附近的同一性一致。在这篇短文中，我们计算了 k ≥ 3 k\geq 3 时的基群 π 1 Diff ∂ ( D 4 k ) \pi _1 \operatorname {Diff}_{\partial }(D^{4k}) 。

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