تقرير
An introduction to knot Floer homology and curved bordered algebras
| العنوان: | An introduction to knot Floer homology and curved bordered algebras |
|---|---|
| المؤلفون: | Alfieri, Antonio, Van Dyke, Jackson |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Mathematics - General Topology |
| الوصف: | We survey Ozsv\'ath-Szab\'o's bordered approach to knot Floer homology. After a quick introduction to knot Floer homology, we introduce the relevant algebraic concepts ($\mathcal{A}_\infty$-modules, type $D$-structures, box tensor, etc.), we discuss partial Kauffman states, the construction of the boundary algebra, and sketch Ozsv\'ath and Szab\'o's analytic construction of the type $D$-structure associated to an upper diagram. Finally we give an explicit description of the structure maps of the $DA$-bimodules of some elementary partial diagrams. These can be used to perform explicit computations of the knot Floer differential of any knot in $S^3$. The boundary DGAs $\mathcal{B}(n,k)$ and $\mathcal{A}(n,k)$ of [7] are replaced here by an associative algebra $\mathcal{C}(n)$. These are the notes of two lecture series delivered by Peter Ozsv\'ath and Zolt\'an Szab\'o at Princeton University during the summer of 2018. Comment: 24 pages, 12 figures, Minor errors have been corrected and the exposition has been improved. To appear in Periodica Mathematica Hungarica |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1811.07348 |
| رقم الأكسشن: | edsarx.1811.07348 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |