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Monday, April 20, 2020 | History

9 edition of Low-dimensional geometry found in the catalog.

Low-dimensional geometry

from Euclidean surfaces to hyperbolic knots

by Francis Bonahon

  • 234 Want to read
  • 23 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Manifolds (Mathematics),
  • Geometry, Hyperbolic,
  • Geometry, Plane,
  • Knot theory

  • Edition Notes

    Includes bibliographical references and index.

    StatementFrancis Bonahon.
    SeriesStudent mathematical library -- v. 49
    Classifications
    LC ClassificationsQA613 .B66 2009
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL23081934M
    ISBN 109780821848166
    LC Control Number2009005856

    1. Low-dimensional topology—Congresses. 2. Symplectic geometry—Congresses. 3. Homol-ogy theory—Congresses. 4. Gauge fields (Physics)—Congresses. I. Ellwood, D. (David), – II. Title. III. Series. QAC55 —dc22 Copying and reprinting. Material in this book may be reproduced by any means for educa-. Francis Bonahon's research is in topology and geometry, with a strong interface with complex analysis and dynamical systems. He specializes in manifolds of dimension two and three. While his early work involved low-dimensional topology and knot theory, his more recent research is centered on hyperbolic geometry and quantum topology.


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Low-dimensional geometry by Francis Bonahon Download PDF EPUB FB2

In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments.

Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic by: Low-Dimensional Geometry book.

Read 2 reviews from the world's largest community for readers. Ships from USA. Start by marking “Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots” as Want to Read: but is almost certainly a much better low-dimensional topologist than him.

Very good introduction to hyperbolic surfaces.3/5. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic : $   This book aims to introduce undergraduate students to some of these important developments.

Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. Low-dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots IAS/Park city mathematical subseries Volume 49 of Student mathematical library Volume 49 of Student mathematical library: IAS/Park City mathematical subseries: Author: Francis Bonahon: Publisher: American Mathematical Soc.

ISBN:Length: pages: Subjects5/5(1). Excellent introduction to the subject of low-dimensional geometry. I read this book as a warm-up for more advanced topics (algebraic topology, hyperbolic knot theory) and was not disappointed.

This book is aimed at advanced undergraduates, but in reality if one has had a good semester of analysis and algebra this book should be very understandable.5/5. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a.

Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry.

However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The first two-thirds of the book is about two-dimensional geometry, focusing mostly on the hyperbolic plane and introducing the basic elements of hyperbolic geometry.

Very quickly the author moves to the construction of locally homogeneous spaces by gluing the sides of a polygon. Textbooks with this kind of geometry are: Michele Audin - Geometry. Elmer Rees - Notes on geometry. Gruenberg, Weir - Linear geometry. Jean Gallier - Geometric Methods and Applications.

Mark Steinberger - A course in low-dimensional geometry. Tarrida - Affine maps, Euclidean motions and Quadrics. Dieudonne - Linear algebra and geometry. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry.

An introduction to contact geometry and topology: What it is Background, fundamental results A major area of research in contemporary low-dimensional geometry and topology Connected to many fields of mathematics: Open book decompositions Knots and links Surfaces in.

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 algebraic geometry and mathematical physics).

Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots About this Title. Francis Bonahon, University of Southern California, Los Angeles, Cited by:   In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds.

This book aims to introduce undergraduate students to some of these 3/5(5). Low-Dimensional Geometry has 4 ratings and 1 review: Published June 1st by American Mathematical Society(RI), pages, Francis Bonahon., English, Book, Illustrated edition: Low-dimensional geometry: from Euclidean surfaces to hyperbolic knots / Francis Bonahon.

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. High dimensional geometry is inherently di↵erent from low-dimensional geometry.

Example 15 Consider how many almost orthogonal unit vectors we can have in space, such that all pairwise angles lie between 88 degrees and 92 degrees. In 0 is some. Note that the plane goes through the origin and contains the vectors and, and therefore contains the points, general equation for a plane can substitute the coordinates of the three points into this equation to get the linear system We can solve the system by substitution to get and, which yields the equation of the plane.

Free Kindle Math Books. Algebra I. Geometry. Trigonometry. Calculus. Advanced Probability and Statistics. More textbooks are available on the CK Foundation site.

Free books Author: Kevin de Asis. Get this from a library. Low-dimensional geometry: from Euclidean surfaces to hyperbolic knots. [Francis Bonahon]. Francis Bonahon – Low Dimensional Geometry - Free ebook download as PDF File .pdf), Text File .txt) or read book online for free.

Undergraduate geometry textbook. The purpose of this book is to give an exposition of the so-called “pseudo-Anosov”theory offoliations of theorygeneralizesThurston’s theory of surface automorphisms, and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Some (but by no means.

Get this from a library. Low-dimensional geometry: from Euclidean surfaces to hyperbolic knots. [Francis Bonahon] -- "The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of.

Low Dimensional Geometry and Topology Special Feature. Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions. Vincent Colin, a, 1 Paolo Ghiggini, a, b and Ko Honda c.

Author information Theorem 6 is proved using standard arguments in symplectic geometry such as those found in Cited by:   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.

collection of documents, web pages or customers. Geometry was added and is extremely useful. Our aim in this book is to present the reader with the mathematical foundations to deal with high-dimensional data.

There are two important parts of this foundation. The rst is high-dimensional geometry along with vectors, matrices, and linear algebra.

Question: TEXTBOOK: Low-Dimensional Geometry Francis Bonahon Problem 1. Let X Be A Regular Decagon (= Polygon With 10 Edges And 10 Vertices)in The Euclidean Plane (R2, Deuc), And Let (¯X, ¯ Deuc) Be The Quotient Space Obtainedby Gluing By Euclidean Translations Opposite Edges.

Review of A Course in the Geometry of n Dimensions. The title of the book, A Course in the Geometry of n Dimensions, is a misnomer on two accounts. First, the book is too small -- 63 pages in all -- for even a 1-semester course.

Second, the book is not about geometry per se. 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. Low-dimensional geometry: from euclidean surfaces to hyperbolic knots The book is published by the American Mathematical Society, in its Student Mathematical Library.

It grew out of my notes for an advanced undergraduate course that I taught at the Park City Mathematical Institute. Buy Low-dimensional Geometry by Francis Bonahon from Waterstones today. Click and Collect from your local Waterstones or get FREE UK delivery on orders over £Author: Francis Bonahon.

Geometry (from the Ancient Greek: γεωμετρία; geo-"earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

Geometry arose independently in a number of early cultures as a practical way for dealing with lengths. The intent is to describe the very strong connection between geometry and low- dimensional topology in a way which will be useful and accessible (with some effort) to graduate students and mathematicians working in related fields, particularly 3-File Size: 1MB.

This book exposes the connection between the low-dimensional orbifold theory and geometry that was first discovered by Thurston in s providing a key tool in his proof of the hyperbolization of Author: Suhyoung Choi.

Michael Kapovich (also Misha Kapovich, Михаил Эрикович Капович, transcription Mikhail Erikovich Kapovich, born ) is a Russian-American mathematician. Kapovich was awarded a doctorate in at the Sobolev Institute of Mathematics in Novosibirsk with thesis advisor Samuel Leibovich Krushkal and thesis "Плоские конформные структуры на 3.

The intent is to describe the very strong connection between geometry and low- dimensional topology in a way which will be useful and accessible (with some effort) to graduate students and mathematicians working in related fields, particularly 3-File Size: 4MB.

Errata for the book Low-dimensional geometry: from euclidean surfaces to hyperbolic knots A somewhat frustrating fact of life is that, however hard you try, it seems impossible to get rid of all misprints and minor mistakes in a math text. This one is no exception.

I am very grateful to Maria Dyachkova, Laure Flapan and, in particular, the. numbers a useful reference is the book by Guillemin and Pollack [9]. The second half of this book is devoted to di erential forms and de Rham cohomology. It begins with an elemtary introduction into the subject and continues with some deeper results such as Poincar e duality, the Cech{de Rham complex, and the Thom isomorphism theorem.

Many of File Size: 1MB. Without question, low dimensional topology is among the most popular areas of mathematics these days. This is altogether reasonable on several counts, including the fact that it resonates with the world of our ordinary experience (at least to some extent: one doesn’t usually encounter the complement of the trefoil knot on the way to the mall), that it allows wonderful pictures.

As pointed out in an earlier comment, low dimensional topology is really really vast and you can spend more than a lifetime reading literature in either dimension 3 or 4. So, try to get some idea from Manolescu's site who is a renowned topologist and focus on a particular topic.The book contains many interesting material on classical synthetic and projective geometry.

Chapters 3, 4 and 5 in his book " Yearning for the Impossible " are also an interesting read. The book " Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots " by F.

Bonahon is excellent and its Chapter 1 to 6 match well with our course. The Arf invariant has higher-order generalizations as do the linking numbers of the components of a link.

Conant et al. use these generalizations to give a nearly complete answer to the problem of classifying the Whitney towers that a link can bound in the 4-ball.A link may not bound disjoint surfaces, and therefore, the authors immerse 2-disks, each of which bounds a component of the link Author: Robion C.

Kirby.