Perturbations of B-type defects in Landau-Ginzburg models are considered. In
particular, the effect of perturbations of defects on their fusion is analyzed
in the framework of matrix factorizations. As an application, it is discussed
how fusion with perturbed defects induces perturbations on boundary conditions.
It is shown that in some classes of models all boundary perturbations can be
obtained in this way. Moreover, a universal class of perturbed defects is
constructed, whose fusion under certain conditions obey braid relations. The
functors obtained by fusing these defects with boundary conditions are twist
functors as introduced in the work of Seidel and Thomas.Comment: 46 page
