Topology of Singular Fibers of Differentiable Maps


Author: Osamu Saeki
Publisher: Springer
ISBN: 3540446486
Category: Mathematics
Page: 154
View: 590

Continue Reading →

The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.

The geometry of topological stability


Author: Andrew Du Plessis,Charles Terence Clegg Wall
Publisher: Oxford University Press, USA
ISBN: 9780198535881
Category: Mathematics
Page: 572
View: 2455

Continue Reading →

The intention of this book is to give the necessary and sufficient conditions for a C map to be C stable, this objective being achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of generic singularities. The methods developed for examining this topology and geometry use results from many areas of mathematics - geometric topology, stratification theory, algebraic geometry, and commutative algebra amoung them, and further progress will doubtless arise from the application of deeper results from theseareas. Conversely, it is to be hoped that they will have interesting consequences for these areas of mathematics, which are those with most interaction with singularity theory. The book describes original research; virtually none of its results have previously appeared elsewhere, either in scientific articles or in books.

Diffeomorphisms of Elliptic 3-Manifolds


Author: Sungbok Hong,John Kalliongis,Darryl McCullough,J. Hyam Rubinstein
Publisher: Springer
ISBN: 364231564X
Category: Mathematics
Page: 155
View: 9208

Continue Reading →

This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small list of known exceptions, is contractible. Considerable foundational and background

Real and Complex Singularities


Author: M. Manoel,M. C. Romero Fuster,C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 1139489917
Category: Mathematics
Page: N.A
View: 2687

Continue Reading →

The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.

Newsletter


Author: New Zealand Mathematical Society
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 5334

Continue Reading →

Surgery and geometric topology

proceedings of the conference held at Josai University, 17-20 September, 1996
Author: Jōsai Daigaku
Publisher: N.A
ISBN: N.A
Category: Algebraic topology
Page: 159
View: 9462

Continue Reading →

Differential geometry

proceedings of the international symposium held at Peñíscola, Spain, October 3-10, 1982
Author: Antonio Martínez Naveira
Publisher: Springer
ISBN: N.A
Category: Mathematics
Page: 194
View: 5538

Continue Reading →