Triangulated categories of singularities and equivalences between   Landau-Ginzburg models
  In this paper we prove an existence of some type of equivalences between triangulated categories of singularities for varieties of different dimensions. This class of equivalences generalizes so called Kn\"orrer periodicity. As consequence we get equivalences between categories of D-branes of type B on Landau-Ginzburg models of different dimensions. 
Dmitri Orlov