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arXiv · 2608.10436

Lower bounds on the number of homotopy types of $\mathrm{SU}(n)$-gauge groups over spheres

Martin Frankland·Yang Hu
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Abstract

We explore the classical question of enumerating the homotopy types of gauge groups of principal $\mathrm{SU}(n)$-bundles over $S^{2m+1}$ in the unstable range $m\geq n$. Using computations of certain $p$-local Samelson products, we obtain lower bounds on the number of such homotopy types. We also present a discussion of the last stable case.

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Martin Frankland, Yang Hu. 2026-08-11. Lower bounds on the number of homotopy types of $\mathrm{SU}(n)$-gauge groups over spheres. https://arxiv.org/abs/2608.10436

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