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Embeddings And Immersions


Author : Masahisa Adachi
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-11-07

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This book covers fundamental techniques in the theory of -imbeddings and -immersions, emphasizing clear intuitive understanding and containing many figures and diagrams. Adachi starts with an introduction to the work of Whitney and of Haefliger on -imbeddings and -manifolds. The Smale-Hirsch theorem is presented as a generalization of the classification of -imbeddings by isotopy and is extended by Gromov's work on the subject, including Gromov's convex integration theory. Finally, as an application of Gromov's work, the author introduces Haefliger's classification theorem of foliations on open manifolds. Also described here is the Adachi's work with Landweber on the integrability of almost complex structures on open manifolds. This book would be an excellent text for upper-division undergraduate or graduate courses.Nothing provided

Encyclopedic Dictionary Of Mathematics


Author : Kiyosi Itô
language : en
Publisher: MIT Press
Release Date : 1993

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Topology And Its Applications


Author : William F. Basener
language : en
Publisher: John Wiley & Sons
Release Date : 2006-11-03

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Discover a unique and modern treatment of topology employing across-disciplinary approach Implemented recently to understand diverse topics, such as cellbiology, superconductors, and robot motion, topology has beentransformed from a theoretical field that highlights mathematicaltheory to a subject that plays a growing role in nearly all fieldsof scientific investigation. Moving from the concrete to theabstract, Topology and Its Applications displays both the beautyand utility of topology, first presenting the essentials oftopology followed by its emerging role within the new frontiers inresearch. Filling a gap between the teaching of topology and its modernuses in real-world phenomena, Topology and Its Applications isorganized around the mathematical theory of topology, a frameworkof rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications incomputer graphics, economics, dynamical systems, condensed matterphysics, biology, robotics, chemistry, cosmology, material science,computational topology, and population modeling, as well as otherareas of science and engineering. Many of these applications arepresented in optional sections, allowing an instructor to customizethe presentation. The author presents a diversity of topological areas, includingpoint-set topology, geometric topology, differential topology, andalgebraic/combinatorial topology. Topics within these areasinclude: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology Special "core intuition" segments throughout the book brieflyexplain the basic intuition essential to understanding severaltopics. A generous number of figures and examples, many of whichcome from applications such as liquid crystals, space probe data,and computer graphics, are all available from the publisher's Website.

Stein Manifolds And Holomorphic Mappings


Author : Franc Forstnerič
language : en
Publisher: Springer
Release Date : 2017-09-05

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This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups./div

Lie Groups And Compact Groups


Author : John F. Price
language : en
Publisher: Cambridge University Press
Release Date : 1977-06-02

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Provides a self-contained introduction to Lie groups and makes results about the structure of Lie groups and compact groups available to a wide audience.

New Perspectives And Challenges In Symplectic Field Theory


Author : Miguel Abreu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

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This volume, in honor of Yakov Eliashberg, gives a panorama of some of the most fascinating recent developments in symplectic, contact and gauge theories. It contains research papers aimed at experts, as well as a series of skillfully written surveys accessible for a broad geometrically oriented readership from the graduate level onwards. This collection will serve as an enduring source of information and ideas for those who want to enter this exciting area as well as for experts.

Algebraic And Geometric Surgery


Author : Andrew Ranicki
language : en
Publisher: Oxford University Press
Release Date : 2002

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'An excellent framework for various courses in Surgery Theory... very readable... I read this fine and carefully written book with great pleasure, and highly recommend it for everyone who wants to undertake a deeper study of Surgery Theory and its Applications.' -Alberto Cavicchioli (Modena), Zentralblatt MATHThis book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, cobordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.