不变性与纽结Floer解立方体
几何拓扑
2014-03-10 v3 量子代数
摘要
本文在纯代数框架下考虑纽结Floer同调的不变性，不涉及Heegaard图、全纯圆盘或网格图。我们证明，(对)Ozsváth和Szabó为纽结Floer同调构造的(经微小修改的)解立方体(该立方体被赋予一个带有基点的辫表示)在类辫Reidemeister移动II和III以及共轭下是不变的。所有移动都假设发生在远离基点的位置。我们还描述了解立方体在稳定化下的行为。这些技术呼应了Khovanov和Rozansky用于证明HOMFLY-PT同调不变性的方法，并进一步证明了这两种理论之间的密切关系。关键思想是证明Murakami-Ohtsuki-Yamada关于HOMFLY-PT多项式的态模型所满足的某些等式的范畴化版本。
引用
@article{arxiv.1007.2609,
title = {Invariance and the knot Floer cube of resolutions},
author = {Allison Gilmore},
journal= {arXiv preprint arXiv:1007.2609},
year = {2014}
}
备注
68 pages, 31 figures; v3 to appear in Quantum Topology; v2 substantially revised from v1 including weakened statement of main result due to error in v1's Lemma 5 (conjugation / moving the basepoint). Other changes: substantial elaboration of argument for Reidemeister 3 invariance, different descriptions of behavior under stabilization and adding/removing layers of marked points