On the Hilbert Polynomial of the HOMFLYPT Homology
classification
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keywords
polynomialhomflypthilberthomologybraidclosedcomponentscontrols
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We prove that the degree of the Hilbert polynomial of the HOMFLYPT homology of a closed braid $B$ is $l-1$, where $l$ is the number of components of $B$. This controls the growth of the HOMFLYPT homology with respect to its polynomial grading. The Hilbert polynomial also reveals a link polynomial hidden in the HOMFLYPT polynomial.
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