Topological Methods In Euclidean Spaces

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Topological Methods In Euclidean Spaces

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Author : Gregory L. Naber
language : en
Publisher: Courier Corporation
Release Date : 2012-08-29

Topological Methods In Euclidean Spaces written by Gregory L. Naber and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.

Extensive development of such topics as elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, and the Stone-Weierstrass Theorem. New section of solutions to selected problems.

Topological Methods In Group Theory

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Author : Ross Geoghegan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-17

Topological Methods In Group Theory written by Ross Geoghegan 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 2007-12-17 with Mathematics categories.

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

Topological Methods In Differential Equations And Inclusions

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Author : Andrzej Granas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Topological Methods In Differential Equations And Inclusions written by Andrzej Granas 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 2012-12-06 with Mathematics categories.

The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.

Topological Methods In Data Analysis And Visualization V

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Author : Hamish Carr
language : en
Publisher: Springer Nature
Release Date : 2020-12-10

Topological Methods In Data Analysis And Visualization V written by Hamish Carr and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-10 with Mathematics categories.

This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms. In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world’s leading experts on topological techniques, the book represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.

Topological Methods In Data Analysis And Visualization Iv

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Author : Hamish Carr
language : en
Publisher: Springer
Release Date : 2017-06-01

Topological Methods In Data Analysis And Visualization Iv written by Hamish Carr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Mathematics categories.

This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volume, resulting from the 2015 TopoInVis workshop held in Annweiler, Germany, will appeal to researchers in the fields of scientific visualization and mathematics, domain scientists with an interest in advanced visualization methods, and developers of visualization software systems.

Geometric And Topological Methods For Quantum Field Theory

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Author : Hernan Ocampo
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-13

Geometric And Topological Methods For Quantum Field Theory written by Hernan Ocampo 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 2005-06-13 with Science categories.

This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.

A First Course In Geometric Topology And Differential Geometry

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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27

A First Course In Geometric Topology And Differential Geometry written by Ethan D. Bloch 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 2011-06-27 with Mathematics categories.

The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.

Topological Methods In Data Analysis And Visualization Vi

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Author : Ingrid Hotz
language : en
Publisher: Springer Nature
Release Date : 2021-09-28

Topological Methods In Data Analysis And Visualization Vi written by Ingrid Hotz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-28 with Mathematics categories.

This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.

Introduction To Symplectic Topology

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Author : Dusa McDuff
language : en
Publisher: Oxford University Press
Release Date : 1998

Introduction To Symplectic Topology written by Dusa McDuff and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

This first edition of this book quickly became an established text in this fast-developing branch of mathematics. This second edition has been significantly revised and expanded. It includes a section on new developments and an expanded discussion of Taubes' and Donaldson's recent results.

Topology Geometry And Gauge Fields

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Author : Gregory L. Naber
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Topology Geometry And Gauge Fields written by Gregory L. Naber 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 2013-03-14 with Mathematics categories.

This volume is intended to carryon the program initiated in Topology, Geometry, and Gauge Fields: Foundations (henceforth, [N4]). It is written in much the same spirit and with precisely the same philosophical motivation: Mathematics and physics have gone their separate ways for nearly a century now and it is time for this to end. Neither can any longer afford to ignore the problems and insights of the other. Why are Dirac magnetic monopoles in one-to-one correspondence with the principal U(l) bundles over S2? Why do Higgs fields fall into topological types? What led Donaldson, in 1980, to seek in the Yang-Mills equations of physics for the key that unlocks the mysteries of smooth 4-manifolds and what phys ical insights into quantum field theory led Witten, fourteen years later, to propose the vastly simpler, but apparently equivalent Seiberg-Witten equations as an alternative? We do not presume to answer these questions here, but only to promote an atmosphere in which both mathematicians and physicists recognize the need for answers. More succinctly, we shall endeavor to provide an exposition of elementary topology and geometry that keeps one eye on the physics in which our concepts either arose in dependently or have been found to lead to a deeper understanding of the phenomena. Chapter 1 provides a synopsis of the geometrical background we assume of our readers (manifolds, Lie groups, bundles, connections, etc. ).