School of Mathematics and Statistics - Research Publications

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Minimal triangulations for an infinite family of lens spaces

Jaco, W ; Rubinstein, H ; Tillmann, S (WILEY, 2009)
FINDING PLANAR SURFACES IN KNOT- AND LINK-MANIFOLDS

Jaco, W ; Rubinstein, JH ; Sedgwick, E (WORLD SCIENTIFIC PUBL CO PTE LTD, 2009-03)

It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. Two similar results are obtained with added boundary conditions. Namely, given a link-manifold M, a component B of ∂M, and a slope γ on B, there is an algorithm to decide if there is an embedded punctured-disk in M with boundary γ and punctures in ∂M\B; and given a link-manifold M, a component B of ∂M, and a meridian slope μ on B, there is an algorithm to decide if there is an embedded punctured-disk with boundary a longitude on B and punctures in ∂M\B. In both cases, if there is one, the algorithm will construct one. The proofs introduce a number of new methods and differ from the classical proofs, using normal surfaces, as solutions may not be found among the fundamental solutions.
Visualizing Ricci flow of manifolds of revolution

Rubinstein, JH ; Sinclair, R (TAYLOR & FRANCIS INC, 2005)
Minimal Surfaces in Geometric 3-Manifolds

RUBINSTEIN, JH (American Mathematical Society, 2005)