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chain complex and quadrilaterals for normal surfaces

Gadgil, Siddhartha and Kalelkar, Tejas (2013) chain complex and quadrilaterals for normal surfaces. In: Rocky Mountain Journal of Mathematics, 43 (2). pp. 479-487.

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Official URL: http://dx.doi.org/10.1216/RMJ-2013-43-2-479

Abstract

We interpret a normal surface in a (singular) three-manifold in terms of the homology of a chain complex. This allows us to study the relation between normal surfaces and their quadrilateral coordinates. Specifically, we give a proof of an (unpublished) observation independently given by Casson and Rubinstein saying that quadrilaterals determine a normal surface up to vertex linking spheres. We also characterize the quadrilateral coordinates that correspond to a normal surface in a (possibly ideal) triangulation.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Rocky Mountain Mathematics Consortium.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Francis Jayakanth
Date Deposited: 20 Sep 2013 12:14
Last Modified: 20 Sep 2013 12:14
URI: http://eprints.iisc.ac.in/id/eprint/47231

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