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

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 $D^b(KQ)$.