A geometric model of tube categories

Details A geometric model of tube categories A geometric model of tube categories

2010-11-02

arxiv.org/abs/1011.0743v2

Mathematics

Representation Theory

13 pages, 6 figures. Reference added in introduction; some small corrections

Scientific paper

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 crossing 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.

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