2004/06/14 by Stephan Tillmann, Tillmann, Stephan
Computer Science · Mathematics · #57M25 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.math/0406271
openalex publication_date 2004/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of a normal surface in a triangulated, compact 3-manifold was generalised by Thurston to a spun-normal surface in a non-compact 3-manifold with ideal triangulation. This paper defines a boundary curve map which takes a spun-normal surface to an element of the direct sum of the first homology groups of the vertex linking surfaces. The boundary curve map is used to study the topology of a spun-normal surface as well as to determine the dimension of the projective solution space of the algebraic equations arising from the quadrilateral coordinates of spun-normal surfaces.