We show that the limiting unicolored
Khovanov–Rozansky chain complex of any infinite positive braid categorifies a
highest-weight projector. This result extends an earlier result of Cautis categorifying
highest-weight projectors using the limiting complex of infinite torus braids.
Additionally, we show that the results hold in the case of colored
homfly–pt
Khovanov–Rozansky homology as well. An application of this result is given in
finding a partial isomorphism between the
homfly–pthomology of any braid
positive link and the stable
homfly–pthomology of the infinite torus knot as
computed by Hogancamp.
Keywords
Khovanov homology, Khovanov–Rozansky homology, link
homology, colored link homology, colored Khovanov–Rozanksy
homology, infinite braids, infinite twist
