Exponential growth of colored HOMFLYPT homology
Abstract
We define reduced colored sl(N) link homologies and use deformation spectral sequences to characterize their dependence on color and rank. We then define reduced colored HOMFLYPT homologies and prove that they arise as large N limits of sl(N) homologies. Together, these results allow proofs of many aspects of the physically conjectured structure of the family of type A link homologies. In particular, we verify a conjecture of Gorsky, Gukov and Stošić about the growth of colored HOMFLYPT homologies.
 Publication:

arXiv eprints
 Pub Date:
 February 2016
 arXiv:
 arXiv:1602.02769
 Bibcode:
 2016arXiv160202769W
 Keywords:

 Mathematics  Geometric Topology;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra;
 57M27
 EPrint:
 39 pages, many figures. v2: version accepted for publication in Advances in Mathematics