Products related to Topology:
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Basic Topology 3 : Algebraic Topology and Topology of Fiber Bundles
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics.It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra.Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number.It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod.It includes more material than is comfortably covered by beginner students in a one-semester course.Students of advanced courses will also find the book useful.This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.
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Homotopical Topology
This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I.M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain.Therefore, this updated English edition will be much welcomed by the mathematical community.Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences.The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).
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Algebraic Topology
Algebraic Topology is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years.Each chapter, or lecture, corresponds to one day of class at SUMaC.The book begins with the preliminaries needed for the formal definition of a surface.Other topics covered in the book include the classification of surfaces, group theory, the fundamental group, and homology. This book assumes no background in abstract algebra or real analysis, and the material from those subjects is presented as needed in the text.This makes the book readable to undergraduates or high-school students who do not have the background typically assumed in an algebraic topology book or class.The book contains many examples and exercises, allowing it to be used for both self-study and for an introductory undergraduate topology course.
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General Topology
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What is a network topology?
A network topology refers to the layout or structure of a computer network. It defines how the different devices, such as computers, servers, and routers, are connected and how data is transmitted between them. Common network topologies include bus, star, ring, and mesh, each with its own advantages and disadvantages in terms of cost, scalability, and fault tolerance. The choice of network topology depends on the specific requirements and constraints of the network environment.
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Can someone explain topology to me?
Topology is a branch of mathematics that deals with the properties of space that are preserved under continuous deformations, such as stretching or bending, but not tearing or gluing. It studies the concept of continuity and connectivity in spaces, focusing on the properties that remain unchanged even when the space is distorted. Topology is concerned with the study of shapes, spaces, and their relationships, without relying on specific measurements like distance or angles. It is a fundamental area of mathematics with applications in various fields such as physics, biology, and computer science.
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Where is which network topology used?
The bus network topology is commonly used in small to medium-sized networks, such as in small businesses or homes. It is cost-effective and easy to set up, making it suitable for these environments. On the other hand, the star network topology is often used in larger networks, such as in corporate environments or data centers. It provides better fault tolerance and scalability, making it a more suitable choice for larger and more complex networks.
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Which book is good for topology?
One highly recommended book for topology is "Topology" by James R. Munkres. This book is widely used in undergraduate and graduate courses in topology and is known for its clear and comprehensive coverage of the subject. It provides a solid foundation in point-set topology and includes a good balance of theory and examples. The book is also praised for its readability and accessibility, making it a popular choice for students and instructors alike.
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Geometry and Topology
Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics.This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples.The treatment emphasises coordinate systems and the coordinate changes that generate symmetries.The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries.Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program.An introduction to basic topology follows, with the Möbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem.Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechanics.A final chapter features historical discussions and indications for further reading.With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics.The book is based on many years' teaching experience, and is thoroughly class-tested.There are copious illustrations, and each chapter ends with a wide supply of exercises.Further teaching material is available for teachers via the web, including assignable problem sheets with solutions.
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Topology And Physics
'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems ...The book explores many interesting and novel topics that lie at the intersection between gravity, quantum fields, condensed matter, physical cosmology and topology ...A rich, well-organized, and comprehensive overview of remarkable and insightful connections between physics and topology is here made available to the physics reader.'Contemporary PhysicsSince its birth in Poincare's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics.As with all beautiful mathematical concepts, topology inevitably - resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences - finds its prominent role in physics.From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'.Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entree toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an apercu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen.We hope that this book will serve to inspire the research community.
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Basic Topology 2 : Topological Groups, Topology of Manifolds and Lie Groups
This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics.It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers.Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis.This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology.It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations.This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.
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Geometry, Topology and Physics
Differential geometry and topology have become essential tools for many theoretical physicists.In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics.Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject.The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories.Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology.The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory.Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems.New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics.The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
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What is the practical relevance of mesh topology?
Mesh topology is highly practical in networking environments where reliability and redundancy are crucial. Its decentralized nature allows for multiple paths for data to travel, reducing the risk of network downtime in case of a link failure. This topology is commonly used in large-scale networks such as telecommunications and data centers where uninterrupted connectivity is essential. Additionally, mesh topology offers scalability as new devices can be easily added without affecting the overall network performance.
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Why is the internet or WLAN a bus topology?
The internet or WLAN is considered a bus topology because all devices are connected to a single communication line, similar to how a bus route connects multiple stops along a single path. In a bus topology, data is transmitted along the communication line, and all devices on the network receive the data, but only the intended recipient processes it. This setup allows for efficient communication between devices and simplifies the network structure, making it easier to add or remove devices without disrupting the entire network.
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With which circuit can one determine a network topology?
One can determine a network topology using a circuit called a "network analyzer." This circuit is designed to analyze the physical and logical layout of a network, including the connections between devices and the flow of data. By using a network analyzer, one can identify the type of network topology being used, such as bus, ring, star, or mesh, and gain insights into the overall structure and performance of the network.
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How do you check the topology of a Blender model?
To check the topology of a Blender model, you can use the Wireframe view mode to see the underlying structure of the mesh. This will allow you to visually inspect the edge flow and vertex distribution of the model. Additionally, you can use the Edit Mode to select and manipulate individual vertices, edges, and faces to ensure they are properly aligned and connected. Finally, you can use the Mesh Analysis tool in Blender to identify any potential issues with the topology, such as non-manifold geometry or overlapping faces.
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