1999/2000 WARWICK SYMPOSIUM ON
GEOMETRY & TOPOLOGY
Organisers: John Jones, Victor Pidstrigatch & Colin Rourke
9-22 July 2000
Workshop on Geometry & Topology
Programme
All talks will be in GLT 3 adjacent in the Mathematics Institute
| Talks arranged to date are: |
| Stefan Bauer |
Title TBA |
| Ralph Cohen |
Mini-course (2 lectures) on the homotopy theory of moduli spaces |
| Oliver Dasbach |
Inequalities for the Thurston norm of link complements
(Joint work with Brian Mangum) Recently, McMullen showed an inequality between the Thurston norm and the Alexander norm of a 3-manifold. This generalizes the well-known fact that twice the genus of a knot is bounded from below by the degree of the Alexander polynomial.
We extend the Bennequin inequality for links to an inequality for all points of the Thurston norm, if the manifold is a link complement.
We discuss the conjectured inequality due to Morton for certain points of the Thurston norm. We prove Morton's conjecture for closed 3-braids. |
| Paul Feehan |
PU(2) monopoles and 4-manifold invariants |
| Ron Fintushel |
Mini-course on 4-manifolds:
1. Smooth Structures on the K3 Surface
2. Surfaces in a Fixed Homology Class
3. The McMullen-Taubes Construction of a 4-Manifold with Inequivalent Symplectic Structures.
|
| Kim Froysov |
A homology cobordism invariant derived from Floer homology |
| Dave Gabai |
Two one and a half hour talks:
1. On the topology of Diff(M^3)
Abstract: We show that if M is a closed hyperbolic manifold, then the space of diffeomorphisms is homotopy equivalent to the isometry group of M.
2. On Poenaru's work on the covering space conjecture.
Abstract: V. Poenaru has announced that the universal covering space of a closed aspherical irreducible 3-manifold is R^3. I will attempt to transmit my understanding of the outline of the proof.
|
| Stavros Garoufalidis |
Homology surgery and invariants of 3-manifolds.
Abstract: We give a rather natural homology surgery problem in the classical dimension. Translating the problem in terms of links, using results of Fenn-Rourke and Kirby, it follows that the vanishing of its obstruction leads to a class diatinguished class of links in a base manifold N. These links define a preferred notion of finite type invariants of 3-manifolds. Using recent technology from this world, under the name of "clasper" or "clover" or "Y-graph", we estimate from above the under of invariants in terms of decorated trivalent graphs. |
| Cameron Gordon |
Title TBA |
| Ian Hambleton |
Topological equivalence of linear representations.
Let G be a finite group and R_TOP(G) the quotient of the real representation ring of G by the equivalence relation V ~ V' iff V direct sum W is G-homeomorphic to V" direct sum W for some representation W. With Erik Pedersen, we recently completed the calculation of R_TOP(G) for G cyclic of 2-power order. This is the first such result for any group that admits non-linear similarities. |
| Thomas Leness |
Title TBA |
| John Luecke |
Strongly n-trivial knots
A knot, k, is called "strongly (n-1)-trivial" if there is a projection of k such that one can choose n crossings of the projection with the property
that making the crossing changes corresponding to any of the 2^n-1 nontrivial combinations of the selected crossings turns the original knot into the unknot. In work with H. Howards we prove that if g is the genus of k, then k fails to be strongly n-trivial for all n, when n is at least 3g-1. |
| Sergei Matveev |
Special spines and a simple invariant of 4-manifolds
Abstract. Based on the notion of a special polyhedron, we present a simplified version of Turaev's shadows of 4-manifolds and construct a simple 4-manifold invariant similar to the epsilon-invariant for 3-manifolds. |
| Blake Mellor |
Intersection graphs and finite type invariants
Chmutov, Duzhin and Lando first suggested studying the chord diagrams which appear in the theory of finite type knot invariants by studying the associated intersection graphs (also known as circle graphs). These graphs retain much (but not all) of the information contained in the chord diagrams. Using this idea, Lando has recently defined a bialgebra of graphs and a natural map to it from the bialgebra of chord diagrams. There are many questions which arise from this construction, such as: What are the kernel and image of the map? What weight systems factor through this map? In this talk I will describe Lando's construction, and how the weight systems arising from some well-known finite type knot invariants factor through Lando's map. I will also give some conjectures about the more difficult questions of the kernel and image of the map. |
| Alex Mijatovic |
Pachner moves and the recognition of the 3-sphere
We describe a procedure to simplify any given triangulation of S^3 using Pachner moves. We obtain an explicit exponential bound on the number of Pachner moves needed for this process. This leads to a new recognition algorithm for the 3-sphere. |
| A.Pajitnov |
Title TBA |
| Elmer Rees |
Title TBA |
| Marty Scharlemann |
Mini-course (3 lectures) on Heegaard splittings |
| David Spring |
Directed embeddings and Eliashberg's folding theorems |
| Morwen Thistlethwaite |
Investigating hyperbolic structures on alternating link complements
A method is examined for determining the hyperbolic structure ofa hyperbolic link complement directly from a diagram. Instead offollowing the more usual practice of looking at shapes of idealtetrahedra, we set up equations involving the shapes of the idealpolygons corresponding to the regions of the diagram; this methodseems peculiarly appropriate to alternating diagrams. There is strong experimental evidence that in a certain sense the hyperbolicmetric for an alternating link complement is not too far removedfrom what one would naively guess after looking at an alternating diagram of the link. |
| Shichweng Wang |
Maps of non-zero degree between 3-manifolds.
Abstract: We will present some examples and facts related the existance of non-zero degree maps between 3-manifolds. |
| Andreas Zastrow |
The higher homology groups of planar sets do not behave anomalously. |
For further information please contact:
Mrs. Peta McAllister, Mathematics Research Centre,
University of Warwick, Coventry CV4 7AL - UK
Phone: 44 + (0)1203 - 524403 Fax: 44 + (0)1203 - 523548
E-mail: peta@maths.warwick.ac.uk |
