Geometric topology. Part 2: 1993 Georgia International by William H. Kazez

By William H. Kazez

This can be half 2 of a two-part quantity reflecting the complaints of the 1993 Georgia foreign Topology convention held on the collage of Georgia throughout the month of August. The texts contain learn and expository articles and challenge units. The convention coated a wide selection of subject matters in geometric topology.
Features:
Kirby's challenge record, which includes an intensive description of the growth made on all the difficulties and encompasses a very entire bibliography, makes the paintings precious for experts and non-specialists who are looking to know about the development made in many components of topology. This checklist may perhaps function a reference paintings for many years to come back.

Gabai's challenge checklist, which makes a speciality of foliations and laminations of 3-manifolds, collects for the 1st time in a single paper definitions, effects, and difficulties that can function a defining resource within the topic region.

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Extra resources for Geometric topology. Part 2: 1993 Georgia International Topology Conference, August 2-13, 1993, University of Georgia, Athens, Georgia

Example text

In fact, Gabai shows that the Gromov norm and the singular Thurston norm of the generator of H2 (∂MK ) are both linear functions of genus K. 42 (Y. Matsumoto) Does the following link in S 3 bound a smooth punctured sphere in B 4 ? If so, (2, 3) ∈ H2 (S 2 × S 2; Z) is represented by a smooth S 2. Can it be represented by a torus? Remarks: This is the simplest unsolved case one encounters in trying to represent (2, 3) ∈ H2 (S 2 × S 2; Z) by a smooth imbedded S 2. This can be done iff such a link as above, with 2 + 2k circles in one group and 3 + 2l circles in the other group oriented to give (2, 3), bounds 30 CHAPTER 1.

One might expect, with a problem list of this size, that the list is all inclusive. Wrong. Of course I have made attempts to cover obvious areas, but I never wished to take on the task of covering everything. For example, laminations are already beautifully covered by Dave Gabai in another problem list in these Proceedings. In the 1977 list, I particularly tried to get problems involving related subjects, but this time, that task was too daunting and no great effort was made. There are not as many problems involving contact structures, graph theory, dynamics, for example, as there could have been.

Update: A proof that v1,0 ≡ 2 (mod 4) is given in [183,Cappell & Shaneson,1984]. 26 (Murasugi) Suppose the first homology group of the 2-fold cyclic branched cover of a knot α ⊂ S 3 is Z/pZ (hence p = |∆α(−1)|), and let Mα be the irregular p-fold dihedral cover of α. Conjecture: If Mα is a Z-homology sphere, then is the signature of α and vi,0 is defined above. r i=1 vi,0 ≡ σ(α) (mod 8) where σ(α) Remarks: The conjecture holds with equality for 2-bridge knots ([450,Hartley & Murasugi, 1978,Canad.

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