We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin-structure is faithful. This paper is designed partly as an introduction to the subject, and much of it should be readable without a background in Floer homology.
We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category such that the homotopy category of this model structure is equivalent to the stable category as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed)...
This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions.
In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković in the course...
An easy explicit construction is given for a full and faithful functor from the bounded derived category of modules over an associative algebra A to the stable category of the repetitive algebra of A. This construction simplifies the one given by Happel.