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### Relative JSJ decompositions

**Geometry/Topology**

Speaker: | BATS at Davis, Peter Scott, Univ of Michigan |

Location: | 1147 MSB |

Start time: | Tue, May 13 2008, 4:00PM |

In the 1970's, Jaco and Shalen, and independently Johannson described their famous decomposition of a Haken 3-manifold which is now known as the JSJ decomposition. One interesting common feature of their proofs is that in order to make their inductive constructions work they needed a relative version of their decomposition. This gives a decomposition of a Haken 3-manifold M relative to a subsurface S of the boundary of M. There has been one topological generalization of the JSJ decomposition to higher dimensions and several somewhat different purely algebraic generalizations, but almost no generalizations of the relative versions of the JSJ decomposition. I will start by discussing the relative JSJ decompositions of 3-manifolds, and then will discuss algebraic generalizations. This is work in progress, joint with Vincent Guirardel and Gadde Swarup.

There will be a dinner after the BATS talks.