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6. Braid varieties


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      Problem 6.1.

      Develop singular braid varieties and relate them to Richardson varieties in $G/P$ and to colored homology.


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          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.


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              Problem 6.3.

              What is the relation between braid varieties and singular braid varieties?


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                  Problem 6.4.

                  Compute $H^*_T(X(\sigma_1\dots\sigma_{n-1})^m\Delta)$.


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                      Problem 6.5.

                      Are there "braid variety analogues" of projectors?


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                          Problem 6.6.

                          Can we determine $gl(m|n)$ / Khovanov homology using braid-like varieties?


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                              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.