Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Metric completions of discrete cluster categories

Methods for generating new triangulated categories from old are notoriously few and far between. Neeman’s recent innovation allows one to complete with respect to suitable metrics on a triangulated category to construct a new triangulated category. This promises the opportunity to construct a plethora of new examples of triangulated categories. However, up to now, explicit computations have all taken place within an existing ambient triangulated category. In this talk, based on joint work with Charley Cummings, we present a cluster-flavoured class of examples of 2-Calabi Yau categories where the computation can be done without this crutch. More specifically, we investigate discrete cluster categories of type A and show that, with a suitable choice of metric, the metric completion of such a category mirrors a topological completion of its combinatorial model.