University of Michigan
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For more information, contact Peter Scott.
If you want to check the list of seminars held in previous terms, click on the appropriate link below.
Fall 2004, Winter 2004, Fall 2003, Winter 2003, Fall 2002, the year 2000-1.
| Date | Speaker | Title (click on title to view abstract) |
| January 7 | NO MEETING | |
| January 14 | NO MEETING | |
| January 21 | NO MEETING | |
| January 28 | NO MEETING | |
| February 4 | NO MEETING | |
| February 11 | NO MEETING |
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| February 18 | Peter Scott, U. of M. | A Relative Annulus Theorem |
| February 25 | NO MEETING | |
| March 4 | NO MEETING | SPRING BREAK |
| March 11 | Dick Canary, U. of M. | Tameness of hyperbolic 3-manifolds |
| March 18 |
NO MEETING | |
| March 25 |
Jean-Francois Lafont (SUNY Binghamton) | Strong Jordan separation and applications to rigidity |
| April 1 |
Eric Zupunski (U. of M.) | Thin Position and Consequences for the JSJ Decomposition |
| April 8 |
NO MEETING | |
| April 15 | Alvaro Pelayo (U. of M.) | Equivariant ball packing of Symplectic Manifolds |
| April 22 | Ravi Shankar (University of Oklahoma) | Dehn functions for finitely presented groups |
In the theory of 3-manifolds, the basic version of the Annulus Theorem considers a 3-manifold M with incompressible boundary, and asserts that if M admits an essential map of an annulus, then M admits an essential embedding of an annulus. However, it is natural to consider situations where M has compressible boundary. In this case one considers an incompressible subsurface S of the boundary of M and restricts attention to annuli in M whose boundary lies in S. There are relative forms of the Annulus Theorem which assert that in most cases, the existence of an essential annulus in M with boundary lying in S implies the existence of an embedded such.
I will discuss the 3-manifold situation with some examples, and will then discuss algebraic versions of these results.
In 1974, Marden conjectured that every hyperbolic 3-manifold with finitely generated fundamental group is topologically tame, i.e. homeomorphic to the interior of a compact 3-manifold. This seemingly purely topological conjecture turned out to have many geometric and analytic consequences and it developed into one of the central conjectures in the study of hyperbolic 3-manifolds.
Recently, Agol and Calegari-Gabai announced proofs of Marden's tameness conjecture. In our talk, we will survey some of the history of the conjecture and its consequences. We will outline a new proof of the conjecture by Soma, which melds the techniques of Agol and Calegari-Gabai.
We will show that, given a continuous map F from S^n to S^{n+1} which contains a topological disk D^n in it's set of injectivity (consisting of points in S^n which are the unique pre-image of their image points), then we have:
(1) that the image F(S^n) separates S^{n+1} into at least two components,
(2) that there are precisely two connected components U, V of S^{n+1}-F(S^n) that contain F(D^n) in their closure, and
(3) that any extension of F to a map G from D^{n+1} to S^{n+1} must surject onto either U or V.
We will then outline how this allows one to prove Mostow type rigidity, and quasi-isometric rigidity for certain singular CAT(-1) spaces.
I will present Scharlemann and Thompson's notion of thin position for 3-manifolds and generalized Heegaard splittings, then describe how this is used to construct bounds on the complexity of the JSJ decomposition of a closed, orientable 3-manifold M. For example, if Theta is the set of canonical tori of M and p is the number of components of M minus Theta, then p is at most 3g-3, where g is the Heegaard genus of M.
A symplectic-toric manifold M is a symplectic 2n-manifold equipped with a Hamiltonian and effective action of a torus of dimension n. The question we address in this talk is:
"Which symplectic-toric 2n-manifolds may be packed by 2n-balls which are embedded in M in a symplectic and equivariant fashion"?
The Dehn function of a finite presentation of a group G = < A | R > gives the least upper bound for the number of relators that must be applied to a word w in G that is trivial i.e., w represents the identity of G, in order to reduce w to the trivial word. Up to a natural equivalence on functions, the Dehn function is a quasi-isometry invariant of the group G. The study of Dehn functions gained importance after Gromov's seminal theorem: a finitely presented group G has sub-quadratic Dehn function if and only if G has linear Dehn function if and only if the Cayley graph of G is delta-hyperbolic.
In this talk we will outline the various definitions and ideas in the subject. Then we will address the basic question: what possible functions can arise as Dehn functions of finitely presented groups? We will outline the construction of the so-called snowflake groups which give many new examples of Dehn functions. The results presented are joint work with Noel Brady, Martin Bridson and Max Forester.
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