Knots, three-manifolds and instantons - Peter Kronheimer (USA) and Tomasz Mrowka (USA)——ICM2018的一小时报告
发文时间：2018-09-28
来源：304am永利集团
Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments, namely the use of Yang-Mills theory, or gauge theory. These techniques were pioneered by Simon Donaldson in his work on 4-manifolds beginning in 1982, but the past ten years have seen new applications of gauge theory, and new interactions with more recent threads in the subject, particularly in 3-dimensional topology and knot theory. In our exploration of this subject, a recurring question will be, "How can we detect knottedness?" Many mathematical techniques have found application to this question, but gauge theory in particular has provided its own collection of answers, both directly and through its connection with other tools. Beyond classical knots, we will also take a look at the nearby but less-explored world of spatial graphs.
https://eta.impa.br/dl/PL014.pdf
本文讨论扭结，三维流形与Floer同调的关系。作者证明了下述两个结果：关于扭结，设K为非平凡扭结，则存在从K的基本群到SO(3)的同态，且像为非交换群; 关于三维流形，其基本群到SO(3)的同态像是非交换群，可以由瞬子Floer同调群的非零性定理得到。
相关附件
11-PL014 Kronheimer and Mrowka
