Celebratio Mathematica — Birman

Complete Bibliography

Works connected to Benson Stanley Farb

Filter the Bibliography List

year	title	people

			clear

J. S. Birman: “The topology of 3-manifolds, Heegaard distance and the mapping class group of a 2-manifold,” pp. 133–149 in Problems on mapping class groups and related topics. Edited by B. Farb. Proceedings of Symposia Pure Mathematics 74. American Mathematical Society (Providence, RI), 2006. MR 2264538 Zbl 1304.57033 incollection

We have had a long-standing interest in the way that structure in the mapping class group of a surface reflects corresponding structure in the topology of 3-manifolds, and conversely. We find this area intriguing because the mapping class group (unlike the collection of closed orientable 3-manifolds) is a group which has a rich collection of subgroups and quotients, and they might suggest new ways to approach 3-manifolds. (For example, it is infinite, non-abelian and residually finite [14]). In the other direction, 3-manifolds have deep geometric structure, for example the struture that is associated to intersections between 2-dimensional submanifolds, and that sort of inherently geometric structure that might bring new tools to bear on open questions regarding the mapping class group. That dual theme is the focus of this article.