Loops of handleslides for sutured diagrams
Geometric Topology
2025-08-07 v1
Abstract
We prove that the cut-system complex of a sutured compression body, with vertices representing cut-systems and edges corresponding to handleslides, becomes simply connected when six kinds of 2-cells are attached. Moreover, we define tight Heegaard invariants and show that each admits a unique extension to a strong Heegaard invariant. This gives a new framework for proving naturality results for Floer homology theories associated to sutured manifolds.
Cite
@article{arxiv.2508.04042,
title = {Loops of handleslides for sutured diagrams},
author = {Qianhe Qin},
journal= {arXiv preprint arXiv:2508.04042},
year = {2025}
}
Comments
26 pages, 20 figures. arXiv admin note: text overlap with arXiv:1210.4996 by other authors