Exponential growth of colored HOMFLY-PT homology

Understand

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 HOMFLY-PT 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 Sto\v{s}i\'c about the growth of colored HOMFLY-PT homologies.