2020/04/23 by Job Daisie Rock, Rock, Job · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2004.11341
This if the final paper in the seriesContinuous Quivers of Type A. In this part, we generalize existing geometric models of type A cluster structures to the new \mathbf E-clusters introduced in part (III). We also introduce an isomorphism of cluster theories and a weak equivalence of cluster theories. Examples of both are given. We use thes geometric models and isomorphisms of cluster theories to begin classifying continuous type A cluster structures. We also introduce a continuous generalization of mutation. This encompasses mutation and (infinite) sequences of mutation. Then we link continuous mutation to our earlier geometric models. Finally, we introduce the space of mutations which generalizes the exchange graph of a cluster structure.