2018/05/13 by Ruizhi Huang, Huang, Ruizhi
Mathematics · Physics and Astronomy · #54C35 #55P15 #55P40 #55R25 #57R19 #57S05 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1805.04879
openalex publication_date 2018/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.