Celebratio Mathematica — Thompson — Complete Bibliography

Complete Bibliography

Works connected to Stephan Tillmann

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J. H. Rubinstein and A. Thompson: “3-manifolds with Heegaard splittings of distance two,” pp. 341–346 in Geometry and topology down under. Edited by C. D. Hodgson, W. H. Jaco, M. G. Scharlemann, and S. Tillman. Contemporary Mathematics 597. American Mathematial Society (Providence, RI), 2013. MR 3186682 incollection

It is well-known that the distance of a Heegard splitting, as defined by Hempel [2001], is related to global properties of the underlying 3-manifold. For example, Casson–Gordon [1987] show that existence of a splitting of distance one implies that the manifold is Haken, i.e. has an embedded incompressible surface. Distance zero splittings are either stabilized, or the underlying manifold is reducible. In this paper, we study the case of distance two splittings. These are interesting as many known examples of splittings of distance greater than one are actually of distance two. Our aim is to describe how simple conditions on a distance two splitting imply interesting properties of the underlying manifold.

J. Hyam Rubinstein	Related	Volume
Martin Scharlemann	Related	Volume
William H. Jaco	Related
Craig David Hodgson	Related
Stephan Tillmann	Related