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arXiv · 1807.01931

Homotopy types of $SU(n)$-gauge groups over non-spin 4-manifolds

Tseleung So
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Abstract

Let $M$ be an orientable, simply-connected, closed, non-spin 4-manifold and let $\mathcal{G}_k(M)$ be the gauge group of the principal $G$-bundle over $M$ with second Chern class $k\in\mathbb{Z}$. It is known that the homotopy type of $\mathcal{G}_k(M)$ is determined by the homotopy type of $\mathcal{G}_k(\mathbb{CP}^2)$. In this paper we investigate properties of $\mathcal{G}_k(\mathbb{CP}^2)$ when $G = SU(n)$ that partly classify the homotopy types of the gauge groups.

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Tseleung So. 2018-07-05. Homotopy types of $SU(n)$-gauge groups over non-spin 4-manifolds. https://arxiv.org/abs/1807.01931

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