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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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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 :

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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.

Progress And Challenges In Dynamical Systems


Author : Santiago Ibáñez
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-20

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This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems. This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.