Bigons, squares, and Combinatorial Floer homology
主 题: Bigons, squares, and Combinatorial Floer homology
报告人: 王家军 博士 (UC Berkeley)
时 间: 2007-03-30 下午 2:30 - 3:30
地 点: 理科一号楼 1114（数学所活动）
Heegaard Floer 同调是三维流形的不变量，同时也给出了四维流形、纽结、接触几何等等几何拓扑不变量。Heegaard Floer理论猜想和Seiberg-Witten理论是等价的，但是定义和计算更加简单，应用也更加广泛一些。Peter Ozsvath和Zoltan Szabo因为提出这个理论而和另外两位拓扑学家分享了今年的Veblen奖。我们将给出这个理论(Hat version)的一个纯组合定义，包括三维流形不变量，纽结不变量等等。这是和Sucharit Sarkar的合作研究。
Heegaard Floer homology is an invariant for closed three-manifolds, which also gives invariants for four-manifolds, knot and links, and contact structures, etc. Conjecturally, Heegaard Floer homology is equivalent to the Seiberg-Witten theory. In this talk, we will give a combinatorial description of the hat version Heegaard Floer homology and the hat version knot Floer homology for any oriented closed three-manifolds and null homologous links. This is joint work with Sucharit Sarkar.
