Derived category invariants andL-series

Invariants of Measure and Category

The purpose of this chapter is to discuss various results concerning the relationship between measure and category. We are mostly interested in set-theoretic properties of these ideals, particularly, their cardinal characteristics. This is a very large area, and it was necessary to make some choices. We decided to present several new results and new approaches to old problems. In most cases we ...

Category O and sl(k) link invariants

The program of categorification via category O was introduced by J. Bernstein, I. Frenkel, and M. Khovanov in [BFK] where tensor powers of the standard two dimensional representation of sl2 were recognized as Grothendieck groups of certain subcategories of O for various gln. They had two different constructions. One was based on studying certain blocks with singular generalized central characte...

Constructible Derived Category

Derived Category of Toric Fibrations

In this paper, we give a structure theorem for the derived category D(X) of a toric fibration X over P with fiber Y provided that Y has a full strongly exceptional collection of line bundles.

Power Series Expansions and Invariants of Links

One may think of Vassiliev invariants (see BN1], B], BL], Ko] and V1,2]) as link invariants with certain nilpotency. From this point of view, it is not surprising that Milnor's link invariants ((M1,2]) are of the same nature as Vassiliev invariants ((BN2], L2]). We give a conceptually clearer proof of this fact here by synthesizing Kontse-vich's construction of Vassiliev invariants and Milnor i...