Geometry Of Spherical Space Form Groups The Second Edition
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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.
The Geometry Of Spherical Space Form Groups
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Author : Peter B. Gilkey
language : en
Publisher: World Scientific
Release Date : 1989
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 with Mathematics categories.
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.
The Geometry Of Spherical Space Form Groups
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Author : Peter B. Gilkey
language : en
Publisher:
Release Date : 2017
The Geometry Of Spherical Space Form Groups written by Peter B. Gilkey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with MATHEMATICS categories.
Aspects Of Differential Geometry V
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Author : Esteban Calviño-Louzao
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Aspects Of Differential Geometry V written by Esteban Calviño-Louzao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.
Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem.
Spectral Geometry Riemannian Submersions And The Gromov Lawson Conjecture
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Author : Peter B. Gilkey
language : en
Publisher: Taylor & Francis
Release Date : 2024-12-15
Spectral Geometry Riemannian Submersions And The Gromov Lawson Conjecture written by Peter B. Gilkey and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-15 with Mathematics categories.
This cutting-edge, standard-setting text explores the spectral geometry of Riemannian submersions. Working for the most part with the form valued Laplacian in the class of smooth compact manifolds without boundary, the authors study the relationship-if any-between the spectrum of Dp on Y and Dp on Z, given that Dp is the p form valued Laplacian and pi: Z (R) Y is a Riemannian submersion. After providing the necessary background, including basic differential geometry and a discussion of Laplace type operators, the authors address rigidity theorems. They establish conditions that ensure that the pull back of every eigenform on Y is an eigenform on Z so the eigenvalues do not change, then show that if a single eigensection is preserved, the eigenvalues do not change for the scalar or Bochner Laplacians. For the form valued Laplacian, they show that if an eigenform is preserved, then the corresponding eigenvalue can only increase. They generalize these results to the complex setting as well. However, the spinor setting is quite different. For a manifold with non-trivial boundary and imposed Neumann boundary conditions, the result is surprising-the eigenvalues can change. Although this is a relatively rare phenomenon, the authors give examples-a circle bundle or, more generally, a principal bundle with structure group G where the first cohomology group H1(G;R) is non trivial. They show similar results in the complex setting, show that eigenvalues can decrease in the spinor setting, and offer a list of unsolved problems in this area. Moving to some related topics involving questions of positive curvature, for the first time in mathematical literature the authors establish a link between the spectral geometry of Riemannian submersions and the Gromov-Lawson conjecture. Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture addresses a hot research area and promises to set a standard for the field. Researchers and applied mathematicians interested in mathematical physics and relativity will find this work both fascinating and important.
Geometry Revealed
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Author : Marcel Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23
Geometry Revealed written by Marcel Berger 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 2010-07-23 with Mathematics categories.
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is t he author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.
Tensor Trigonometry
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Author : Ninul A.S.
language : en
Publisher: Fizmatkniga
Release Date :
Tensor Trigonometry written by Ninul A.S. and has been published by Fizmatkniga this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The Tensor Trigonometry, with revealing a tensor nature of the angles and their functions and added by differential trigonometry, is developed for wide applications in various fields. Planimetry includes metric part and trigonometry. In geometries of metric spaces from the end of XIX age their tensor forms are widely used. Trigonometry was remaining in its scalar flat forms. Tensor Trigonometry is its development from Leonard Euler classic forms into spatial k-dimensional (at k > 2) tensor forms with vector and scalar orthoprojections, with step by step increasing a complexity and opportunities. Described in the book are fundamentals of this new mathematical subject with many initial examples of applications. In theoretic plan, Tensor Trigonometry complements naturally Analytic Geometry and Linear Algebra. In practical plan, it gives the clear tools for analysis and solutions of various geometric and physical problems in homogeneous isotropic spaces, as Euclidean, quasi- and pseudo-Euclidean ones, on perfect surfaces of constant radius embedded into them with n-D non-Euclidean Geometries, and in Theory of Relativity. So, it gives classic projective models of non-Euclidean Geometries as trigonometric ones, general laws of summing two-steps and polysteps motions in complete differential and integral forms with polar decomposition of the sum into principal and induced orthospherical motions. The applications were developed till the differential tensor trigonometry of world lines and curves in 3D and 4D pseudo- and quasi- Euclidean spaces, in addition, to the classic Frenet-Serret theory, with absolute and relative differential-geometric parameters of curves, main kinematic and dynamical characteristics of a body moving in space-time along a world line with 4-velocity of Poincare. Due to our tensor trigonometric approach, clear explanations of all well-known and new STR and GR relativistic effects are given with physical interpretations in full agreement with the Law of Energy-Momentum conservation, Quantum Mechanics, Noether Theorem and Higgs Theory. The Tensor Trigonometry can be useful in various domains of mathematics and physics. It is intended to researchers in the fields of analytic geometry of any dimension, linear algebra with matrix theory, non-Euclidean geometries, theory of relativity, quantum mechanics and to all those who is interested in new knowledges and applications, given by exact sciences. It may be useful for educational purposes with this new math subject in the university and graduate schools departments of algebra, geometry and physics - relativistic and classical. The 1st edition of the Tensor Trigonometry was published by the main Russian scientific publishing house "MIR" in October 2004 - ISBN 10: 5030037179 (for instance, A. S. Ninul "Tenzornaja trigonometrija" in SUB.Uni-Goettingen.de and WorldCat OCLC 255128609). It was reviewed by the Moscow State University professor, Dr.Sc. M. M. Postnikov and by the Moscow Regional University professor, Dr.Sc. О. V. Manturov. This 3rd edition is a renovation of previous two in 2004) (by MIR) and in 2021 (by Fizmatlit).
Categorical Decomposition Techniques In Algebraic Topology
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Author : Gregory Arone
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Categorical Decomposition Techniques In Algebraic Topology written by Gregory Arone and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms".
Noncommutative Geometry And The Standard Model Of Elementary Particle Physics
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Author : Florian Scheck
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-11-26
Noncommutative Geometry And The Standard Model Of Elementary Particle Physics written by Florian Scheck 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 2002-11-26 with Science categories.
The outcome of a close collaboration between mathematicians and mathematical physicists, these Lecture Notes present the foundations of A. Connes noncommutative geometry, as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.
Aspects Of Boundary Problems In Analysis And Geometry
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Author : Juan Gil
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Aspects Of Boundary Problems In Analysis And Geometry written by Juan Gil and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Boundary problems constitute an essential field of common mathematical interest. The intention of this volume is to highlight several analytic and geometric aspects of boundary problems with special emphasis on their interplay. It includes surveys on classical topics presented from a modern perspective as well as reports on current research. The collection splits into two related groups: - analysis and geometry of geometric operators and their index theory - elliptic theory of boundary value problems and the Shapiro-Lopatinsky condition