Baur, K orcid.org/0000-0002-7665-476X and Marsh, RJ orcid.org/0000-0002-4268-8937 (2012) A geometric model of tube categories. Journal of Algebra, 362. pp. 178-191. ISSN 0021-8693
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.
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Keywords: | primary; 16G10; 16G20; 16G70; 18E30; 14C17; secondary; 13F60 | ||||
Dates: |
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Institution: | The University of Leeds | ||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 22 Aug 2019 15:28 | ||||
Last Modified: | 22 Aug 2019 15:28 | ||||
Status: | Published | ||||
Publisher: | Elsevier | ||||
Identification Number: | https://doi.org/10.1016/j.jalgebra.2012.04.009 | ||||
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