Higher Groups in Higher Gauge Theory
Time: 2018-09-25
Published By: He Liu
Speaker(s): Chenchang Zhu (Georg-August-Universität Göttingen)
Time: 14:00-16:00 October 11, 2018
Venue: Room 77201, Jingchunyuan 78, BICMR
There has been much recent development on higher symmetries in topological orders as the study of topological phase of maters has become a very active field in condensed matter physics. In this talk, we will carry out the mathematical foundation of a recent joint project with Tian Lan and Xiao-Gang Wen in the above direction. Higher groups are group objects in a higher category. In a very concise way, they can be realised as a simplicial object satisfying suitable Kan conditions. We will give a more explicit algebraic model to realise some of them. This model is between the target of Dold-Kan functor and the skeleton case. Then we discuss higher gauge theory for topological orders, classification of them in lower dimensions, and explicit realisations in special cases.
