On the computation of torus link homology
Ben Elias, Matthew Hogancamp
TL;DR
This paper presents a novel computational approach for triply graded link homology, specifically tailored for torus links, providing exact results for (n,n)-torus links and confirming related conjectures.
Contribution
Introduces a new method for computing triply graded link homology, with exact solutions for all (n,n)-torus links and verification of existing conjectures.
Findings
Exact homology computations for all (n,n)-torus links
Verification of conjectures relating homology and Hilbert schemes
Enhanced understanding of torus link homology structure
Abstract
We introduce a new method for computing triply graded link homology, which is particularly well-adapted to torus links. Our main application is to the (n,n)-torus links, for which we give an exact answer for all n. In several cases, our computations verify conjectures of Gorsky et al relating homology of torus links with Hilbert schemes.
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