The Geometry Of Spherical Space Form Groups
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The Geometry Of Spherical Space Form Groups
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Author : Peter B Gilkey
language : en
Publisher: World Scientific
Release Date : 1989-09-01
The Geometry Of Spherical Space Form Groups written by Peter B Gilkey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-09-01 with Mathematics categories.
New Edition: The Geometry of Spherical Space Form Groups (2nd Edition)In this volume, the geometry of spherical space form groups is studied using the eta invariant. The author reviews the analytical properties of the eta invariant of Atiyah-Patodi-Singer and describes how the eta invariant gives rise to torsion invariants in both K-theory and equivariant bordism. The eta invariant is used to compute the K-theory of spherical space forms, and to study the equivariant unitary bordism of spherical space forms and the Pinc and Spinc equivariant bordism groups for spherical space form groups. This leads to a complete structure theorem for these bordism and K-theory groups.There is a deep relationship between topology and analysis with differential geometry serving as the bridge. This book is intended to serve as an introduction to this subject for people from different research backgrounds.This book is intended as a research monograph for people who are not experts in all the areas discussed. It is written for topologists wishing to understand some of the analytic details and for analysists wishing to understand some of the topological ideas. It is also intended as an introduction to the field for graduate students.
Geometry Of Spherical Space Form Groups The Second Edition
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Author : Peter B Gilkey
language : en
Publisher: World Scientific
Release Date : 2018-01-04
Geometry Of Spherical Space Form Groups The Second Edition written by Peter B Gilkey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-04 with Mathematics categories.
This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.
Mathematics Unlimited 2001 And Beyond
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Author : Björn Engquist
language : en
Publisher: Springer
Release Date : 2017-04-05
Mathematics Unlimited 2001 And Beyond written by Björn Engquist and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Mathematics categories.
This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty.
Selected Papers Of Morikazu Toda
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Author : Morikazu Toda
language : en
Publisher: World Scientific
Release Date : 1993
Selected Papers Of Morikazu Toda written by Morikazu Toda and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
This volume contains selected papers of Dr Morikazu Toda. The papers are arranged in chronological order of publishing dates. Among Dr Toda's many contributions, his works on liquids and nonlinear lattice dynamics should be mentioned. The one-dimensional lattice where nearest neighboring particles interact through an exponential potential is called the Toda lattice which is a miracle and indeed a jewel in theoretical physics. The papers in this volume can be grouped into five subjects: statistical mechanics, theory of liquids and solutions, lattice dynamics, Toda lattice and soliton theory and its applications.
Selected Papers Of Wilhelm P A Klingenberg
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Author : Wilhelm P A Klingenberg
language : en
Publisher: World Scientific
Release Date : 1991-11-18
Selected Papers Of Wilhelm P A Klingenberg written by Wilhelm P A Klingenberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-18 with Mathematics categories.
This set of selected papers of Klingenberg covers some of the important mathematical aspects of Riemannian Geometry, Closed Geodesics, Geometric Algebra, Classical Differential Geometry and Foundations of Geometry of Klingenberg. Of significance were his contributions to Riemannian Geometry in the Large which opened a new area in Global Riemannian Geometry. He also introduced the Hilbert manifold of closed curves of class H1 on a Riemannian manifold. In connection with his work in closed geodesics, he became interested in the properties of the geodesic flow. Classical results from dynamical systems became useful tools for the study of closed geodesics. He was also credited for drawing closer together Riemannian Geometry and Hamiltonian systems, which had developed separately since the time of H Poincaré.Besides publishing research papers, Klingenberg also wrote a dozen books and lecture notes, among which is the important reference work “Riemannsche Geometrie im Groβen”.
Boundary Value Problems For Analytic Functions
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Author : Jian-ke Lu
language : en
Publisher: World Scientific
Release Date : 1994-02-04
Boundary Value Problems For Analytic Functions written by Jian-ke Lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-04 with Mathematics categories.
This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincaré-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter I describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals; Chapters II and III study, respectively, fundamental boundary value problems and their applications to singular integral equations for closed contours; Chapters IV and V discuss the same problems for curves with nodes (including open arcs); Chaper VI deals with similar problems for systems of functions; Chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of these exercises.For graduate students or seniors, all the 7 chapters can be used for a full year course, while the first 3 chapters may be used for a one-semester course.
The Mathematical Structure Of Stable Physical Systems
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Author : Dr. Martin Concoyle & G.P. Coatmundi
language : en
Publisher: Trafford Publishing
Release Date : 2014
The Mathematical Structure Of Stable Physical Systems written by Dr. Martin Concoyle & G.P. Coatmundi and has been published by Trafford Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Education categories.
This book is an introduction to the simple math patterns used to describe fundamental, stable spectral-orbital physical systems (represented as discrete hyperbolic shapes), the containment set has many-dimensions, and these dimensions possess macroscopic geometric properties (which are also discrete hyperbolic shapes). Thus, it is a description which transcends the idea of materialism (ie it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy, and which has a natural structure for memory, where this construct is made in relation to the main property of the description being, in fact, the spectral properties of both material systems and of the metric-spaces which contain the material systems, where material is simply a lower dimension metric-space, and where both material-components and metric-spaces are in resonance with the containing space. Partial differential equations are defined on the many metric-spaces of this description, but their main function is to act on either the, usually, unimportant free-material components (to most often cause non-linear dynamics) or to perturb the orbits of the, quite often condensed, material trapped by (or within) the stable orbits of a very stable hyperbolic metric-space shape.
Conformal Riemannian And Lagrangian Geometry
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Author : Sun-Yung A. Chang
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Conformal Riemannian And Lagrangian Geometry written by Sun-Yung A. Chang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactificationsof manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially inconnection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus of variations. The lectures provide an up-do-date overview and an introduction to the research literature in each of their areas. The book is a very enjoyable read, which should prove useful to graduate students and researchers in differential geometryand geometric analysis.
Representation Theory Of Lie Groups And Lie Algebras Proceedings Of Fuji Kawaguchiko Conference
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Author : Takeshi Kawazoe
language : en
Publisher: World Scientific
Release Date : 1992-08-07
Representation Theory Of Lie Groups And Lie Algebras Proceedings Of Fuji Kawaguchiko Conference written by Takeshi Kawazoe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-07 with categories.
The proceedings in this volume covers recent developments of representation theory of real Lie groups, Lie algebras, harmonic analysis on homogeneous spaces, their applications and related topics.
Conf Rence Mosh Flato 1999
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Author : Giuseppe Dito
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Conf Rence Mosh Flato 1999 written by Giuseppe Dito and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Mathematics categories.
These two volumes constitute the Proceedings of the `Conférence Moshé Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity. With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena. Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.