PreprintCC BY 4.0arXiv
Minimal slN Complexes of Rational Tangles via the Fukaya Category
Abstract
We compute minimal slN complexes for oriented rational tangles, denoted [ [τu/vO] ]N, in terms of the topological Fukaya category of the $3$-punctured disk. This demonstrates that the complexes stabilize, allowing us to define a HOMFLY-PT homology for rational tangles.
Related
- The Relative Fukaya Category as a Closed-Open Deformation
- Symplectomorphism invariance of the wrapped Fukaya category
- Fukaya category with supports
- One-periodic category of twisted complexes, Cohen-Macaulay modules and differential modules
- Day Convolution and Homotopy Groups on the Pointed Homotopy Category of CW Complexes
BibTeX
@misc{higgins2026minimal,
title = {{Minimal $\mathfraksl_N$ Complexes of Rational Tangles via the Fukaya Category}},
author = {Jonathan A. Higgins},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20558},
eprint = {2610.20558},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20558},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimal sl_N Complexes of Rational Tangles via the Fukaya Category
AU - Jonathan A. Higgins
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20558
UR - https://arxiv.org/abs/2610.20558
AB - We compute minimal sl_N complexes for oriented rational tangles, denoted [ [τ_u/v^O] ]_N, in terms of the topological Fukaya category of the $3$-punctured disk. This demonstrates that the complexes stabilize, allowing us to define a HOMFLY-PT homology for rational tangles.
ER -