星形图谱的Koszul对偶$\mathcal{A}_{\infty}$代数 -- 第一部分
几何拓扑
2025-10-14 v2 辛几何
摘要
通过对给定3流形的Heegaard图进行特定切割,可以构建-双模,其张量积可恢复原始3流形的Heegaard Floer homology.第一步是为每个切割对应的代数进行构建.本文使用Lipshitz、Ozsv\'ath和Thurston引入的-结构图形计算法,为特定星形类切割构建Koszul对偶加权-代数和,以及双模.随后将在续集中证明该对偶结果.
引用
@article{arxiv.2408.01564,
title = {Koszul dual $\mathcal{A}_{\infty}$ algebras for star-shaped diagrams -- Part 1},
author = {Isabella Khan},
journal= {arXiv preprint arXiv:2408.01564},
year = {2025}
}
备注
73 pages, many figures; this revision removes the statement and proof of the main duality result, which are to appear in a separate paper, along with several auxiliary definitions