6. Braid varieties

Problem 6.1.
Develop singular braid varieties and relate them to Richardson varieties in $G/P$ and to colored homology. 
Problem 6.2.
What properties of braid varieties in $G/B$ should survive in $G/P$? In other words, what properties of full flag varieties remain in partial flag varieties. 
Problem 6.7.
Define the analogues of braid varieties for $sl_N$ homology, and study their connection with representation varieties.
Cite this as: AimPL: Algebra, geometry, and combinatorics of link homology, available at http://aimpl.org/agclinkhom.