Grid diagrams in Heegaard Floer theory
Ciprian Manolescu
TL;DR
This paper reviews how grid diagrams are used in Heegaard Floer theory, focusing on combinatorial constructions, algorithms for unknot detection, and the computability of invariants for 3- and 4-manifolds.
Contribution
It provides a comprehensive overview of grid diagram techniques and their applications in computing Heegaard Floer invariants.
Findings
Constructed combinatorial link Floer complex
Developed algorithm for unknot detection
Showed invariants are algorithmically computable (mod 2)
Abstract
We review the use of grid diagrams in the development of Heegaard Floer theory. We describe the construction of the combinatorial link Floer complex, and the resulting algorithm for unknot detection. We also explain how grid diagrams can be used to show that the Heegaard Floer invariants of 3-manifolds and 4-manifolds are algorithmically computable (mod 2).
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Taxonomy
TopicsGeometric and Algebraic Topology · Botulinum Toxin and Related Neurological Disorders · Topological and Geometric Data Analysis