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Homotopy types of gauge groups over Riemann surfaces

Masaki Kameko, Daisuke Kishimoto and Masahiro Takeda

Algebraic & Geometric Topology 23 (2023) 2309–2327
Abstract

Let G be a compact connected Lie group with π1(G). We study the homotopy types of gauge groups of principal G–bundles over Riemann surfaces. This can be applied to an explicit computation of the homotopy groups of the moduli spaces of stable vector bundles over Riemann surfaces.

Keywords
gauge group, Riemann surface, stable vector bundle, Samelson product
Mathematical Subject Classification
Primary: 57S05
Secondary: 55Q15
References
Publication
Received: 3 August 2021
Revised: 6 February 2022
Accepted: 8 March 2022
Published: 25 July 2023
Authors
Masaki Kameko
Department of Mathematical Sciences
Shibaura Institute of Technology
Saitama
Japan
Daisuke Kishimoto
Faculty of Mathematics
Kyushu University
Fukuoka
Japan
Masahiro Takeda
Department of Mathematics
Kyoto University
Kyoto
Japan

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