2 edition of Aspects of low dimensional manifolds found in the catalog.
Aspects of low dimensional manifolds
|Statement||edited by Y. Matsumoto, S. Morita.|
|Series||Advanced studies in pure mathematics -- 20|
|Contributions||Matsumoto, Yukio., Morita, S.|
Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifold. Article in Journal of Machine Learning Research 4(2) . This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for.
Recent success with the four-dimensional Poincaré conjecture has revived interest in low-dimensional topology, especially the three-dimensional Poincaré conjecture and other aspects of the problems of classifying three-dimensional manifolds. For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the largest and least well-understood class of compact 3-manifolds. Familiar and new tools from diverse areas of mathematics /5(2).
These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact. Topological Aspects of Low-dimensional Systems: Proceedings, Les Houches Summer School of Theoretical Physics, Session Les Houches, France, July
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Contains topics that include knots and links, three-dimensional hyperbolic geometry, conformally flat structures on three-manifolds, Floer homology, and the geometry and topology of four-manifolds.
This book is of interest to mathematicians, physicists, graduate students, and others seeking a good introduction to the field. "The aim of this fine book is to study the algorithmic topology of low-dimensional manifolds.
The book is written in a very accurate and readable style. It looks like as a selfcontained and fundamental work on Aspects of low dimensional manifolds book algorithmic 3-dimensional topology both for graduate students and researchers.
4/5(1). Topology of Low-Dimensional Manifolds Proceedings of the Second Sussex Conference, Editors: Fenn, R. (Ed.) Free Preview. Book description This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects interact (for example: topology, differential and.
Recent success with the four-dimensional Poincaré conjecture has revived interest in low-dimensional topology, especially the three-dimensional Poincaré conjecture and other aspects of the problems of classifying three-dimensional manifolds.
These problems have a driving force, and have generated a great body of research, as well as insight. Abstract. This chapter discusses the working range of low-rank models and how to extend them. It further discusses the future work in low-rank models, including low-rank models for tensorial data, nonlinear manifold clustering, and randomized algorithms, which encourages the.
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, /5.
While such data is often high-dimensional, it is of interest to approximate it with a low-dimensional or even one-dimensional space, since many important aspects of data are often intrinsically low-dimensional.
Furthermore, there are many scenarios where the underlying structure is graph-like, e.g, river/road networks or various trajectories. Analogously to the classification of manifolds, in high codimension (meaning more than 2), embeddings are classified by surgery, while in low codimension or in relative dimension, they are rigid and geometric, and in the middle (codimension 2), one has.
underlying manifold. Many types of high dimensional data can be characterized in this way— for example, images generated by different views of the same three dimensional object.
Beyond applications in machine learning and pattern recognition, the use of low dimensional manifolds toFile Size: 5MB. It assembles research papers which reflect diverse currents in low-dimensional topology.
The topology of 3-manifolds, hyperbolic geometry and knot theory emerge as major themes. The inclusion of surveys of work in these areas should make the book very useful to students as well as researchers. viii PREFACE a very modest way.
John Etnyre and Lenhard Ng's Problems in low dimensional contact topology is a new list assembled for these proceedings. It is a product of two problem sessions held at the conference, one on 3-dimensional contact topology led.
Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics.
The subject of the book is the topology of bare 3-manifolds, without geometric structures, which became incorporated into 3-dimensional topology by the work of Thurston.
This non-geometric part of low-dimensional topology is presented by Matveev in a truly geometric : Springer-Verlag Berlin Heidelberg. of manifolds are the curves and the surfaces and these were quite well understood.
Riemann was the ﬁrst to note that the low dimensional ideas of his time were particular aspects of a higher dimensional world. The ﬁrst chapter of this book introduces the reader to the concept of smooth manifold. The Conference was devoted to a broad spectrum of topics in Low-Dimensional Topology.
However, special emphasis was given to hyperbolic and combinatorial structures, minimal surface theory, negatively curbed groups, group actions on R-trees, and gauge theoretic aspects of 3-manifolds.
Recent results in these topics are published : Hardcover. Embedding manifolds to low-dimensional spaces provides a way to explicitly model such manifolds. Learning motion manifolds can be achieved through linear subspace approximation (PCA), as in Fablet and Black ().
This volume consists of ten original papers written by experts in various aspects of low dimensional topology. The topics covered by them include knots and links, 3-dimensional hyperbolic geometry, conformally flat structures on 3-manifolds, Floer homology, the geometry and topology of 4-manifolds.
The Conference was devoted to a broad spectrum of topics in Low-Dimensional Topology. However, special emphasis was given to hyperbolic and combinatorial structures, minimal surface theory, negatively curbed groups, group actions on R-trees, and gauge theoretic aspects of 3-manifolds.
Recent results in these topics are published here. Low-dimensional topology—Congresses. Symplectic geometry—Congresses. Homol-ogy theory—Congresses. Gauge ﬁelds (Physics)—Congresses.
Ellwood, D. (David), – II. Title. III. Series. QAC55 —dc22 Copying and reprinting. Material in this book may be reproduced by any means for educa.
Special cases of manifolds are the curves and the surfaces and these were quite well understood. B. Riemann was the ﬁrst to note that the low dimensional ideas of his time were particular aspects of a higher dimensional world.
The ﬁrst chapter of this book introduces the reader to the concept of smooth manifold through.The approach to equilibrium for systems of reaction−diffusion equations on bounded domains is studied geometrically.
It is shown that equilibrium is approached via low-dimensional manifolds in the infinite-dimensional function space for these dissipative, parabolic systems. The fundamental aspects of this process are mapped out in some detail for single species cases Cited by: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics.
Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and 5/5(1).