Author: Osamu Saeki

Publisher: Springer

ISBN: 3540446486

Category: Mathematics

Page: 154

View: 9088

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.
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Author: Toshisumi Fukui,Shuichi Izumiya,Satoshi Koike,Toshisumi Fukuda

Publisher: CRC Press

ISBN: 9780582328747

Category: Mathematics

Page: 232

View: 7474

This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.
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Author: Tim Poston,Ian Stewart

Publisher: Courier Corporation

ISBN: 0486143783

Category: Mathematics

Page: 512

View: 761

First integrated treatment of main ideas behind René Thom's theory of catastrophes stresses detailed applications in the physical sciences. Mathematics of theory explained with a minimum of technicalities. Over 200 illustrations clarify text designed for researchers and postgraduate students in engineering, mathematics, physics and biology. 1978 edition. Bibliography.
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Author: Sungbok Hong,John Kalliongis,Darryl McCullough,J. Hyam Rubinstein

Publisher: Springer

ISBN: 364231564X

Category: Mathematics

Page: 155

View: 7130

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
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Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2656

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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: 3921

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