Knot Floer homology and the fundamental group of $ (1,1) $ knots

TL;DR

This paper presents an algorithm to compute the knot Floer homology of (1,1) knots directly from a specific presentation of their fundamental group, linking algebraic and topological invariants.

Contribution

It introduces a novel algorithm that connects fundamental group presentations to knot Floer homology for (1,1) knots, enabling new computational approaches.

Findings

Algorithm effectively computes knot Floer homology from fundamental group presentations.

Establishes a direct method linking algebraic and topological knot invariants.

Facilitates further research in knot theory and low-dimensional topology.

Abstract

We give an algorithm for computing the knot Floer homology of a $ (1,1) $ knot from a particular presentation of its fundamental group.