Celebratio Mathematica — Rubinstein

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Works connected to Saburo Matsumoto

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I. R. Aitchison, S. Matsumoto, and J. H. Rubinstein: “Immersed surfaces in cubed manifolds,” Asian J. Math. 1 : 1 (1997), pp. 85–95. MR 1480991 Zbl 0935.57033 article

We investigate the separability of the canonical surface immersed in cubed manifolds of non-positive curvature, partially answering the hyperbolicity question of cubed 3-manifolds. We show that the canonical surface is separable if we assume that the degrees of all edges are even. Further, the general argument also gives the same result for higher-dimensional manifolds admitting a cubing of non-positive curvature. This main result is extended to some other structures, including flying-saucer and polyhedral decompositions as well as surgeries on certain link complements; these constructions provide examples of non-Haken manifolds that are virtually Haken.

Iain Roderick Aitchison	Related
Saburo Matsumoto	Related

I. R. Aitchison, S. Matsumoto, and J. H. Rubinstein: “Surfaces in the figure-8 knot complement,” J. Knot Theory Ramifications 7 : 8 (1998), pp. 1005–1025. MR 1671559 Zbl 0924.57018 article

Iain Roderick Aitchison	Related
Saburo Matsumoto	Related

I. R. Aitchison, S. Matsumoto, and J. H. Rubinstein: “Dehn surgery on the figure 8 knot: Immersed surfaces,” Proc. Am. Math. Soc. 127 : 8 (1999), pp. 2437–2442. MR 1485454 Zbl 0926.57006 article

Iain Roderick Aitchison	Related
Saburo Matsumoto	Related