Homotopy of gauge groups over non-simply connected five-dimensional manifolds  

作　　者：Ruizhi Huang 

机构地区：[1]Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2021年第5期1061-1092,共32页中国科学：数学（英文版）

基　　金：supported by Postdoctoral International Exchange Program for Incoming Postdoctoral Students under Chinese Postdoctoral Council and Chinese Postdoctoral Science Foundation, Chinese Postdoctoral Science Foundation (Grant No.2018M631605);National Natural Science Foundation of China (Grant No.11801544)。

摘　　要：Both the gauge groups and 5-manifolds are important in physics and mathematics. In this paper,we combine them to study the homotopy aspects of gauge groups over 5-manifolds. For principal bundles over non-simply connected oriented closed 5-manifolds of a certain type, we prove various homotopy decompositions of their gauge groups according to different geometric structures on the manifolds, and give the partial solution to the classification of the gauge groups. As applications, we estimate the homotopy exponents of their gauge groups, and show periodicity results of the homotopy groups of gauge groups analogous to the Bott periodicity.Our treatments here are also very effective for rational gauge groups in the general context, and applicable for higher dimensional manifolds.

关 键 词：gauge group 5-manifolds homotopy decompositions homotopy exponents homotopy groups rational homotopy theory Bott periodicity 

分 类 号：O152[理学—数学]