2012/09/10 by Kiyoshi Igusa, Gordana Todorov, Igusa, Kiyoshi +1 · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.1209.1879
In arXiv:1209.0038 we constructed topological triangulated categories Cc as stable categories of certain topological Frobenius categories Fc. In this paper we show that these categories have a cluster structure for certain values of c including c=pi. The continuous cluster categories are those Cc which have cluster structure. We study the basic structure of these cluster categories and we show that Cc is isomorphic to an orbit category Dr/Fs of the continuous derived category Dr if c=r pi/s. In Cpi, a cluster is equivalent to a discrete lamination of the hyperbolic plane. We give the representation theoretic interpretation of these clusters and laminations.