Topology of Singular Fibers of Differentiable Maps

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

Real Analytic and Algebraic Singularities

Author: Toshisumi Fukui,Shuichi Izumiya,Satoshi Koike,Toshisumi Fukuda
Publisher: CRC Press
ISBN: 9780582328747
Category: Mathematics
Page: 232
View: 6388

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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.

Catastrophe Theory and Its Applications

Author: Tim Poston,Ian Stewart
Publisher: Courier Corporation
ISBN: 0486143783
Category: Mathematics
Page: 512
View: 4711

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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.

Diffeomorphisms of Elliptic 3-Manifolds

Author: Sungbok Hong,John Kalliongis,Darryl McCullough,J. Hyam Rubinstein
Publisher: Springer
ISBN: 364231564X
Category: Mathematics
Page: 155
View: 3583

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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

Surgery and geometric topology

proceedings of the conference held at Josai University, 17-20 September, 1996
Author: Jōsai Daigaku
Publisher: N.A
Category: Algebraic topology
Page: 159
View: 9808

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