Homotopy Types of Gauge Groups Over Non-Simplyconnected Closed 4-Manifolds

So, Tse Leung

doi:10.1017/s0017089518000241

Cited by 13 publications

(14 citation statements)

References 21 publications

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“…By the previous computations of homotopy groups, we see that ΣM 4 in general is not a bouquet of Moore spaces while Σ 2 M 4 indeed is, i.e., [43]). Let X be a stable CW -complex with cell structure…”

Section: Suspension Homotopy Type Of 5-manifoldsmentioning

confidence: 73%

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Homotopy of gauge groups over non-simply-connected five-dimensional manifolds

Huang

2019

Sci. China Math.

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Both the gauge groups and 5-manifolds are important in physics and mathematics. In this paper, we combine them together to study the homotopy aspects of gauge groups over 5-manifolds. For principal bundles over non-simply connected oriented closed 5-manifolds of certain type, we prove various homotopy decompositions of their gauge groups according to different geometric structures on the manifolds, and give partial solution to the classification of the gauge groups. As applications, we estimate the homotopy exponents of their gauge groups, and show periodicity results of the homotopy groups of gauge groups analogous to Bott periodicity. Our treatments here are also very effective for rational gauge groups in general context, and applicable for higher dimensional manifolds.

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Section: Suspension Homotopy Type Of 5-manifoldsmentioning

confidence: 73%

“…When n = 3, π 4 (P 3 (c)) = 0 by Lemma 3.3 of [43] and π 3 (P 3 (c)) ∼ = Z/c by Lemma 3.2. Hence π 4 (P 3 (c); Z/c) ∼ = Z/c.…”

Section: Suspension Homotopy Type Of 5-manifoldsmentioning

confidence: 94%

Homotopy of gauge groups over non-simply-connected five-dimensional manifolds

Huang

2019

Sci. China Math.

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“…A fundamental result of Crabb and Sutherland [6] claims that although there may be infinitely many isomorphism classes of principal G-bundles over X, their gauge groups have only finitely many distinct homotopy types. The explicit classifications of homotopy types of gauge groups were investigated particularly for S 4 by Kono [23], Hasui-Kishimoto-Kono-Sato [18], Theriault [38], etc., and more generally for 4-manifolds by Theriault [37], So [33] and So-Theriault [34]. Moreover, Theriault [37] and West [41] studied the homotopy decompositions of c The Author(s), 2021.…”

Section: Introductionmentioning

confidence: 99%

“…The basic idea to study the homotopy types of gauge groups over these manifolds, as applied in the work of Theriault [37] and So [33], is to decompose them into smaller and simpler pieces. It is a classical result that the isomorphism classes of Gprincipal bundles over a compact manifold M are classified by the set of homotopy classes of classifying maps [M, BG].…”

Section: Introductionmentioning

confidence: 99%

Homotopy of gauge groups over high-dimensional manifolds

Huang¹

2021

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high-dimensional manifolds. To be more specific, we study gauge groups of bundles over (n − 1)-connected closed 2n-manifolds, the classification of which was determined by Wall and Freedman in the combinatorial category. We also investigate the gauge groups of the total manifolds of sphere bundles based on the classical work of James and Whitehead. Furthermore, other types of 2n-manifolds are also considered. In all the cases, we show various homotopy decompositions of gauge groups. The methods are combinations of manifold topology and various techniques in homotopy theory.

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“…Compared to the extensive work on G k (S 4 ), only two cases of G k (CP 2 ) have been studied, which are the SU (2)and SU (3)-cases [12,18]. As a sequel to [14], this paper investigates the homotopy types of G k (CP 2 )'s in order to explore gauge groups over non-spin 4manifolds.…”

Section: Introductionmentioning

confidence: 99%