A geometric model of tube categories
Representation Theory
2020-12-21 v3 Differential Geometry
Abstract
We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension groups of degree 1 between indecomposable objects in terms of negative geometric intersection numbers between corresponding arcs, giving a geometric interpretation of the description of an extension group in the cluster category of a tube as a symmetrized version of the extension group in the tube. We show that a similar result holds for finite dimensional representations of the linearly oriented quiver of type A-double-infinity.
Keywords
Cite
@article{arxiv.1011.0743,
title = {A geometric model of tube categories},
author = {Karin Baur and Bethany Marsh},
journal= {arXiv preprint arXiv:1011.0743},
year = {2020}
}
Comments
15 pages, 7 figures. Discussion of maximal rigid objects and triangulations at end of Section 3. Minor corrections