Abstract
Categorification of quantum group representations and its application in low-dimensional topology
Mikhail Khovanov
Columbia University
We will survey known and conjectural realizations of finite-dimensional
representations of simple Lie algebras and quantum groups as Grothendieck
groups of abelian and triangulated categories. These constructions should
lead to a lift of quantum polynomials of links to cohomology theories of links
and invariants of link cobordisms.
representations of simple Lie algebras and quantum groups as Grothendieck
groups of abelian and triangulated categories. These constructions should
lead to a lift of quantum polynomials of links to cohomology theories of links
and invariants of link cobordisms.
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