由幂零切片辛几何得到的链环不变量
辛几何
2007-05-23 v3 几何拓扑
表示论
摘要
利用某些在李理论中自然出现的流形的辛几何，我们定义了一种不变量，将分次阿贝尔群赋予有向链环。相关流形是 sl_{2m} 内某些幂零轨道的横向切片，以及这些切片与正则半单轨道的交。该不变量被猜想等于 Khovanov 的组合定义的同调理论（该理论的重分次以某种方式塌缩）。
引用
@article{arxiv.math/0405089,
title = {A link invariant from the symplectic geometry of nilpotent slices},
author = {Paul Seidel and Ivan Smith},
journal= {arXiv preprint arXiv:math/0405089},
year = {2007}
}
备注
v2: minor change to the introduction (grading in the long exact sequence corrected). v3: referees' suggestions and corrections incorporated; major changes to section 2 (the general Lie theory simplified by narrowing scope to sl_n) and minor changes to section 4 (more background on Floer theory included). This version to appear in Duke Mathematical Journal