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 Stošić about the growth of colored HOMFLY-PT homologies.
- Pub Date:
- February 2016
- Mathematics - Geometric Topology;
- High Energy Physics - Theory;
- Mathematics - Quantum Algebra;
- 39 pages, many figures. v2: version accepted for publication in Advances in Mathematics