Loops of handleslides for sutured diagrams

Qianhe Qin

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arXiv · 2508.04042

Loops of handleslides for sutured diagrams

Qianhe Qin

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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.

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Qianhe Qin. 2025-08-06. Loops of handleslides for sutured diagrams. https://arxiv.org/abs/2508.04042

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