The HOMFLY polynomial for links is defined in terms of its skein relation, which is a certain linear relation describing the behavior of this invariant under crossing changes. This linear relation is categorified by a certain fundamental distinguished triangle relating Rouquier complexes, in the category of Soergel bimodules. In this talk I will discuss an extension of these ideas to the “colored” HOMFLY polynomial, and its categorification via singular Soergel bimodules. The familiar distingushed triangle gets replaced a longer one-sided twisted complex, and consequently the “link-splitting properties” of colored HOMFLY invariants are somewhat more subtle than their standardly colored progenitor. This is joint work with David Rose and Paul Wedrich.
A skein relation for singular Soergel bimodules
11.05.2021 15:00 - 16:30
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location:
Meeting ID: 431 655 310, Passcode: 0cnL5d