We first revisit knot theory from the perspective of embedding spaces. We will focus on paths and loops in knot spaces. One-cocycles are important tools to distinguish them up to homotopy.  Among these,  combinatorial 1-cocycles introduced by Thomas Fiedler are of particular interest. In this talk, I will present some recent progress on combinatorial 1-cocycles on the space of long knots, using the 1-cocycles of order 4 as examples. I will show that the 1-cohomology classes represented by some of them descend to the space of oriented closed knots.

报告人简介：

张卜天, 武大数院2017级本科生. 目前在法国图卢兹大学工作，从事代数相关数学研究。