Homotopy types of gauge groups related to S3-bundles over S4
Homotopy types of gauge groups related to S3-bundles over S4
Let Ml,m be the total space of the S3-bundle over S4 classified by the element lσ+mρ∈π4(SO(4)), l,m∈Z. In this paper we study the homotopy theory of gauge groups of principal G-bundles over manifolds Ml,m when G is a simply connected simple compact Lie group such that π6(G)=0. That is, G is one of the following groups: SU(n) (n≥4), Sp(n) (n≥2), Spin(n) (n≥5), F4, E6, E7, E8. If the integral homology of Ml,m is torsion-free, we describe the homotopy type of the gauge groups over Ml,m as products of recognisable spaces. For any manifold Ml,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.
Gauge groups, Homotopy decompositions, Principal bundles, Sphere bundles
56-85
Membrillo-Solis, Ingrid
c458faf5-8cdb-4618-ba90-f8a90209f20a
15 March 2019
Membrillo-Solis, Ingrid
c458faf5-8cdb-4618-ba90-f8a90209f20a
Membrillo-Solis, Ingrid
(2019)
Homotopy types of gauge groups related to S3-bundles over S4.
Topology and its Applications, 255, .
(doi:10.1016/j.topol.2019.01.004).
Abstract
Let Ml,m be the total space of the S3-bundle over S4 classified by the element lσ+mρ∈π4(SO(4)), l,m∈Z. In this paper we study the homotopy theory of gauge groups of principal G-bundles over manifolds Ml,m when G is a simply connected simple compact Lie group such that π6(G)=0. That is, G is one of the following groups: SU(n) (n≥4), Sp(n) (n≥2), Spin(n) (n≥5), F4, E6, E7, E8. If the integral homology of Ml,m is torsion-free, we describe the homotopy type of the gauge groups over Ml,m as products of recognisable spaces. For any manifold Ml,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.
Text
Revised_GaugeG_2
- Accepted Manuscript
More information
Accepted/In Press date: 12 January 2019
e-pub ahead of print date: 22 January 2019
Published date: 15 March 2019
Keywords:
Gauge groups, Homotopy decompositions, Principal bundles, Sphere bundles
Identifiers
Local EPrints ID: 428189
URI: http://eprints.soton.ac.uk/id/eprint/428189
ISSN: 0166-8641
PURE UUID: 352c13c2-26f9-4d45-9012-c36fd37a13e4
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Date deposited: 14 Feb 2019 17:30
Last modified: 16 Mar 2024 07:33
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