On connections on principal bundles

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• 作者：Indranil Biswas¹ ; ^{indranil@math.tifr.res.in}
• 关键词：Principal bundle ; Universal connection ; Holomorphic connection ; Real Higgs bundle
• 刊名：Arab Journal of Mathematical Sciences
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：32-43
• 全文大小：241 K
• 卷排序：23

文摘

A new construction of a universal connection was given in Biswas, Hurtubise and Stasheff (2012). The main aim here is to explain this construction. A theorem of Atiyah and Weil says that a holomorphic vector bundle EE over a compact Riemann surface admits a holomorphic connection if and only if the degree of every direct summand of EE is zero. In Azad and Biswas (2002), this criterion was generalized to principal bundles on compact Riemann surfaces. This criterion for principal bundles is also explained.