Publications (59)
The Thurston norm via spun-normal immersions
Daryl Cooper, Stephan Tillmann, William Worden
A theory of transversely oriented spun-normal immersed surfaces in ideally triangulated 3--manifolds is developed in this paper, including linear functionals determining the bounda…
Multisections of piecewise linear manifolds
J. Hyam Rubinstein, Stephan Tillmann
Recently Gay and Kirby described a new decomposition of smooth closed -manifolds called a trisection. This paper generalises Heegaard splittings of -manifolds and trisections…
An algorithm for the Euclidean cell decomposition of a cusped strictly convex projective surface
Stephan Tillmann, Sampson Wong
Cooper and Long generalised Epstein and Penner's Euclidean cell decomposition of cusped hyperbolic manifolds of finite volume to non-compact strictly convex projective manifolds of…
Z2-Thurston Norm and Complexity of 3-Manifolds
William Jaco, J. Hyam Rubinstein, Stephan Tillmann
A new lower bound on the complexity of a 3-manifold is given using the Z2-Thurston norm. This bound is shown to be sharp, and the minimal triangulations realising it are characteri…
Degenerations of ideal hyperbolic triangulations
Stephan Tillmann
Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on…
Slope norm and an algorithm to compute the crosscap number
William Jaco, J. Hyam Rubinstein, Jonathan Spreer +1
We give three algorithms to determine the crosscap number of a knot in the 3-sphere using -efficient triangulations and normal surface theory. Our algorithms are shown to be cor…