Gadgil, Siddhartha; Kalelkar, Tejas A chain complex and quadrilaterals for normal surfaces. (English) Zbl 1270.57061 Rocky Mt. J. Math. 43, No. 2, 479-487 (2013). Summary: 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 Specifically, we give a proof of an (unpublished) observation independently given by Casson and Rubinstein saying that quadrilaterals determine a normal surface up to vertex linking spheres.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. MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57Q15 Triangulating manifolds 52B70 Polyhedral manifolds Keywords:normal surface; three manifold; quadrilateral coordinates; vertex linking spheres PDFBibTeX XMLCite \textit{S. Gadgil} and \textit{T. Kalelkar}, Rocky Mt. J. Math. 43, No. 2, 479--487 (2013; Zbl 1270.57061) Full Text: DOI arXiv Euclid