Differentiable Periodic Maps

Differentiable Periodic Maps
Author: Pierre E. Conner
Publisher: Springer Science & Business Media
Total Pages: 155
Release: 2013-12-14
Genre: Mathematics
ISBN: 3662416336

This research tract contains an exposition of our research on bordism and differentiable periodic maps done in the period 1960-62. The research grew out of the conviction, not ours alone, that the subject of transformation groups is in need of a large infusion of the modern methods of algebraic topology. This conviction we owe at least in part to Armand Borel; in particular Borel has maintained the desirability of methods in transformation groups that use differentiability in a key fashion [9, Introduction], and that is what we try to supply here. We do not try to relate our work to Smith theory, the homological study of periodic maps due to such a large extent to P. A. Smith; for a modern development of that subject which expands it greatly see the Borel Seminar notes [9]. It appears to us that our work is independent of Smith theory, but in part inspired by it. We owe a particular debt to G. D. Mostow, who pointed out to us some time ago that it followed from Smith theory that an involution on a compact manifold, or a map of prime period [italic lowercase]p on a compact orientable manifold, could not have precisely one fixed point. It was this fact that led us to believe it worthwhile to apply cobordism to periodic maps.

Differentiable Periodic Maps

Differentiable Periodic Maps
Author: P. E. Conner
Publisher: Springer
Total Pages: 186
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540350322

MEMS Vibratory Gyroscopes provides a solid foundation in the theory and fundamental operational principles of micromachined vibratory rate gyroscopes, and introduces structural designs that provide inherent robustness against structural and environmental variations. In part one, the dynamics of the vibratory gyroscope sensing element is developed, common micro-fabrication processes and methods commonly used in inertial sensor production are summarized, design of mechanical structures for both linear and torsional gyroscopes are presented, and electrical actuation and detection methods are discussed along with details on experimental characterization of MEMS gyroscopes. In part two, design concepts that improve robustness of the micromachined sensing element are introduced, supported by constructive computational examples and experimental results illustrating the material. MEMS Vibratory Gyroscopes is a must have book for engineers in both industry and academia who specialize in the design and manufacture of gyroscopes. Readers will find: A unique balance between theory and practical design issues. Comprehensive and detailed information outlining the mathematical models of the mechanical structure and system-level sensor design. Solid background Information on mechanical and electrical design, fabrication, packaging, testing and characterization. About The MEMs Reference Shelf: "The MEMs Reference Shelf is a series devoted to Micro-Electro-Mechanical Systems (MEMs) which combine mechanical, electrical, optical, or fluidic elements on a common microfabricated substrate to create sensors, actuators, and microsystems. The series, authored by leading MEMs practitioners, strives to provide a framework where basic principles, known methodologies and new applications are integrated in a coherent and consistent manner." STEPHEN D. SENTURIA Massachusetts Institute of Technology, Professor of Electrical Engineering, Emeritus

Topology of Singular Fibers of Differentiable Maps

Topology of Singular Fibers of Differentiable Maps
Author: Osamu Saeki
Publisher: Springer
Total Pages: 146
Release: 2004-08-30
Genre: Mathematics
ISBN: 3540446486

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.

Singularities of Differentiable Maps

Singularities of Differentiable Maps
Author: V.I. Arnold
Publisher: Springer Science & Business Media
Total Pages: 390
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461251540

... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).

Bordism, Stable Homotopy and Adams Spectral Sequences

Bordism, Stable Homotopy and Adams Spectral Sequences
Author: Stanley O. Kochman
Publisher: American Mathematical Soc.
Total Pages: 294
Release: 1996
Genre: Mathematics
ISBN: 9780821806005

This book is a compilation of lecture notes that were prepared for the graduate course ``Adams Spectral Sequences and Stable Homotopy Theory'' given at The Fields Institute during the fall of 1995. The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy theory, such as the nilpotence and periodicity theorems. Suitable as a text for an intermediate course in algebraic topology, this book provides a direct exposition of the basic concepts of bordism, characteristic classes, Adams spectral sequences, Brown-Peterson spectra and the computation of stable stems. The key ideas are presented in complete detail without becoming encyclopedic. The approach to characteristic classes and some of the methods for computing stable stems have not been published previously. All results are proved in complete detail. Only elementary facts from algebraic topology and homological algebra are assumed. Each chapter concludes with a guide for further study.