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Homotopy of gauge groups over high-dimensional manifolds

Published online by Cambridge University Press:  05 February 2021

Ruizhi Huang*
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing100190, China (


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.

Research Article
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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