Homotopy type of gauge groups of quaternionic line bundles over spheres

Claudio, Mario Henrique Andrade; Spreafico, Mauro

doi:10.1016/j.topol.2008.08.016

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Cited by 4 publications

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“…Since Kono [12] solved this problem for principal SU(2)-bundles over S 4 , many solutions have been produced for special G and K [1,[6][7][8][9]16]. However, as one can imagine, the above problem is quite difficult before localizing relevant spaces.…”

Section: Introductionmentioning

confidence: 99%

On p-local homotopy types of gauge groups

Kishimoto¹,

Kono²,

Tsutaya³

2014

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Section: Introductionmentioning

confidence: 99%

On p-local homotopy types of gauge groups

Kishimoto¹,

Kono²,

Tsutaya³

2014

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Homotopy types of $${{\textrm{Spin}}}^{{\textrm{c}}}(n)$$-gauge groups over $$S^4$$

Rea

2023

European Journal of Mathematics

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The gauge group of a principal G-bundle P over a space X is the group of G-equivariant homeomorphisms of P that cover the identity on X. We consider the gauge groups of bundles over $$S^4$$ S 4 with $${{\textrm{Spin}}}^{{\textrm{c}}}(n)$$ Spin c ( n ) , the complex spin group, as structure group and show how the study of their homotopy types reduces to that of $${{\textrm{Spin}}}(n)$$ Spin ( n ) -gauge groups over $$S^4$$ S 4 . We then advance on what is known by providing a partial classification for $${{\textrm{Spin}}}(7)$$ Spin ( 7 ) - and $${{\textrm{Spin}}}(8)$$ Spin ( 8 ) -gauge groups over $$S^4$$ S 4 .

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Homotopy types of gauge groups related to S3-bundles over S4

Solis¹

2019

Topology and its Applications

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Let M l,m be the total space of the S 3-bundle over S 4 classified by the element lσ + mρ ∈ π 4 (SO(4)), l, m ∈ Z. In this paper we study the homotopy theory of gauge groups of principal G-bundles over manifolds M l,m when G is a simply connected simple compact Lie group such that π 6 (G) = 0. That is, G is one of the following groups: SU (n) (n ≥ 4), Sp(n) (n ≥ 2), Spin(n) (n ≥ 5), F 4 , E 6 , E 7 , E 8. If the integral homology of M l,m is torsion-free, we describe the homotopy type of the gauge groups over M l,m as products of recognisable spaces. For any manifold M l,m with non-torsion-free homology, we give a p-local homotopy decomposition, for a prime p ≥ 5, of the loop space of the gauge groups.

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Homotopy type of gauge groups of quaternionic line bundles over spheres

Cited by 4 publications

References 6 publications

On p-local homotopy types of gauge groups

On p-local homotopy types of gauge groups

Homotopy types of $${{\textrm{Spin}}}^{{\textrm{c}}}(n)$$-gauge groups over $$S^4$$

Homotopy types of gauge groups related to S3-bundles over S4

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