Mathematics > Algebraic Topology
arXiv:2606.01903 (math)
[Submitted on 1 Jun 2026]
Abstract:In this paper, we study the space of compactly supported embeddings between Euclidean spaces, $\mathrm{Emb}_c(\mathbb{R}^j, \mathbb{R}^n)$. By utilizing hairy graphs, we construct elements in the homotopy groups $\pi_{\bullet}(\overline{\mathrm{Emb}}_c(\mathbb{R}^j, \mathbb{R}^{n})) \otimes \mathbb{Q}$ corresponding to certain uni-trivalent graphs in the model. We then prove that these elements are nontrivial. Consequently, we show that the rational homotopy groups of $\mathrm{Emb}_c(\mathbb{R}^{n-2}, \mathbb{R}^n)$ are infinite-dimensional in infinitely many degrees when $n \ge 5$ is odd.
Submission history
From: Daiki Irikura [view email]
[v1]
Mon, 1 Jun 2026 08:42:47 UTC (553 KB)
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