Shifting numbers in triangulated categories via bounded t-structures

Abstract

The shifting numbers measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category, and are analogous to Poincare translation numbers that are widely used in dynamical systems. One of the ways to define these invariants is via the phase functions of Bridgeland stability conditions. We show in this short note that the shifting numbers can also be defined via the bounded t-structures. In particular, the full package of stability conditions (a bounded t-structure, and a central charge on a charge lattice) is not necessary for the purpose of computing the shifting numbers