TL;DR
This paper demonstrates that the module structure on link Floer homology can detect whether a link is split, extending similar detection results to sutured Floer homology.
Contribution
It establishes that the module structure on link Floer homology detects split links and extends this detection to sutured Floer homology, building on prior work.
Findings
Link Floer homology detects split links.
Sutured Floer homology detection result established.
Extension of detection results to sutured Floer homology.
Abstract
Inspired by work of Lipshitz-Sarkar, we show that the module structure on link Floer homology detects split links. Using results of Ni, Alishahi-Lipshitz, and Lipshitz-Sarkar, we establish an analogous detection result for sutured Floer homology.
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