TL;DR
This paper introduces a grid presentation for singular links and extends link Floer homology to these links, proving its consistency and acyclicity under certain conditions.
Contribution
It is the first to define a grid presentation for singular links and generalize link Floer homology to this class, establishing foundational properties.
Findings
Homology is consistent and well-defined for singular links.
Under certain conditions, the homology is acyclic.
Euler characteristic of the homology vanishes in specific cases.
Abstract
We define a grid presentation for singular links i.e. links with a finite number of rigid transverse double points. Then we use it to generalize link Floer homology to singular links. Besides the consistency of its definition, we prove that this homology is acyclic under some conditions which naturally make its Euler characteristic vanish.
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