Classification of co-slicings and co-t-structures for the Kronecker algebra

TL;DR

This paper introduces a new concept of 'generalised' co-slicings in triangulated categories, classifies them for the Kronecker algebra, and uses this to classify co-t-structures and compute the co-stability manifold.

Contribution

It defines 'generalised' co-slicings, extends the theory of co-stability conditions, and provides a complete classification for the Kronecker algebra's derived category.

Findings

Classified 'generalised' co-slicings in D^b(KQ)

Classified co-t-structures in D^b(Q)

Computed the co-stability manifold of D^b(KQ)

Abstract

In this paper we introduce the notion of a 'generalised' co-slicing of a triangulated category. This generalises the theory of co-stability conditions in a manner analogous to the way in which Gorodentsev, Kuleshov and Rudakov's t-stabilities generalise Bridgeland's theory of stability conditions. As an application of this notion, we use a complete classification of 'generalised' co-slicings in the bounded derived category of the Kronecker algebra, $D^b(KQ)$, to obtain a classification of co-t-structures in $D^b(Q)$. This is then used to compute the co-stability manifold of $D^b(KQ)$.