2008/10/02 by Siddhartha Gadgil, Gadgil, Siddhartha, Tejas Kalelkar +1
Computer Science · Mathematics · #57Q35 (Primary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.0810.0342
openalex publication_date 2008/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 co-ordinates. Specifically, we give a proof of an (unpublished) observation independently given by Casson and Rubinstein saying that quadrilaterals determine a normal surface up to vertex linking spheres.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 characterise the quadrilateral coordinates that correspond to a normal surface in a (possibly ideal) triangulation.