By William H. Kazez
This can be half 2 of a two-part quantity reflecting the lawsuits of the 1993 Georgia foreign Topology convention held on the college of Georgia through the month of August. The texts comprise learn and expository articles and challenge units. The convention lined a large choice of subject matters in geometric topology.
Features:
Kirby's challenge checklist, which includes an intensive description of the development made on all the difficulties and encompasses a very entire bibliography, makes the paintings necessary for experts and non-specialists who are looking to find out about the development made in many parts of topology. This checklist may possibly function a reference paintings for many years to come back.
Gabai's challenge record, which specializes in foliations and laminations of 3-manifolds, collects for the 1st time in a single paper definitions, effects, and difficulties which can function a defining resource within the topic region.
Read Online or Download Geometric topology. Part 2: 1993 Georgia International Topology Conference, August 2-13, 1993, University of Georgia, Athens, Georgia PDF
Similar topology books
Whitehead G. W. Homotopy thought (MIT, 1966)(ISBN 0262230194)(1s)_MDat_
The Hypoelliptic Laplacian and Ray-Singer Metrics
This booklet provides the analytic foundations to the speculation of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator performing on the cotangent package deal of a compact manifold, is meant to interpolate among the classical Laplacian and the geodesic move. Jean-Michel Bismut and Gilles Lebeau determine the elemental useful analytic homes of this operator, that's additionally studied from the viewpoint of neighborhood index conception and analytic torsion.
This publication provides the 1st steps of a concept of confoliations designed to hyperlink geometry and topology of 3-dimensional touch constructions with the geometry and topology of codimension-one foliations on 3-dimensional manifolds. constructing virtually independently, those theories first and foremost look belonged to 2 diversified worlds: the idea of foliations is a part of topology and dynamical platforms, whereas touch geometry is the odd-dimensional 'brother' of symplectic geometry.
- The Classification of Knots and 3-Dimensional Spaces (Oxford Science Publications)
- Lectures on the ?2-Sobolev Theory of the ?-Neumann problem
- Infinite-dimensional dynamical systems
- Topological Dimension and Dynamical Systems (Universitext)
Extra info for Geometric topology. Part 2: 1993 Georgia International Topology Conference, August 2-13, 1993, University of Georgia, Athens, Georgia
Sample text
43 (Scharlemann) Are there knots f : S 1 → S 3 such that for any locally flat concordance F : S 1 × I → S 3 × I the map π1 (S 3 − f(S 1)) → π1(S 3 × I − F (S 1 × I)) is injective? Conjecture: This is true for torus knots. Remarks: This is true for torus knots if F must be a fibered concordance. Update: The conjecture is true [187,Casson & Gordon,1983,Invent. ]. 44 (Kauffman) Does link concordance imply link homotopy? ) Update: Yes, [379,Giffen,1979,Math. ] and [388,Goldsmith,1979,Comment. Math.
The knot is composite or cable iff the complement of K, C 3(K), admits a proper imbedding of an annulus A that is essential in the sense that (i) π1(A) → π1 (C 3(K)) is monic, and (ii) A cannot be pushed into ∂C 3(K) by a homotopy fixing ∂A; then K is composite if a boundary curve of A generates H1 (C 3(K)) and is cable otherwise [999,Simon,1973,Ann. ]. Suppose π1 (C 3(K)) ∼ = π1 (C 3(L)). If C 3 (K) has no essential annulus, then C 3(K) is 3 homeomorphic to C (L) [303,Feustel,1976,Trans. Amer.
Note that if a knot has a Seifert matrix of the form ( B0 C0 ), then its Alexander polynomial is one. Hence, define a good boundary link to be one for which there is a summand Ai ⊂ H1 (Fi ; Z) such that 2 dim Ai = dim H1 (Fi ; Z) and the intersection of every element of Ai and every other element of H1 (Fj ; Z) is zero for all i, j. 25 Question. Is a good boundary link slice? Note that a slice link is not necessarily a boundary link [1008,Smythe,1966]. Update: All Alexander polynomial one knots are topologically slice.