Topology category: 256 books

Cover of A Guide to the Classification Theorem for Compact Surfaces
by Jean Gallier, Dianna Xu
Language: English
Release Date: February 5, 2013

This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive...
Cover of Algebraic Topology
by Edwin H. Spanier
Language: English
Release Date: December 6, 2012

This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds....
Cover of Euler's Gem

Euler's Gem

The Polyhedron Formula and the Birth of Topology

by David S. Richeson, David S. Richeson
Language: English
Release Date: July 23, 2019

How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From...
Cover of Morse Theory

Morse Theory

Smooth and Discrete

by Kevin P Knudson
Language: English
Release Date: May 29, 2015

Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the...
Cover of Knots and Physics
by Louis H Kauffman
Language: English
Release Date: November 9, 2012

This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics...
Cover of Topological and Statistical Methods for Complex Data

Topological and Statistical Methods for Complex Data

Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces

by
Language: English
Release Date: November 19, 2014

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges...
Cover of Rational Homotopy Theory and Differential Forms
by Phillip Griffiths, John Morgan
Language: English
Release Date: October 2, 2013

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth...
Cover of Topology, Geometry and Gauge fields
by Gregory L. Naber
Language: English
Release Date: September 24, 2010

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them...
Cover of The Geometry of Celestial Mechanics
by Hansjörg Geiges
Language: English
Release Date: March 24, 2016

Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia...
Cover of Boolean Representations of Simplicial Complexes and Matroids
by John Rhodes, Pedro V. Silva
Language: English
Release Date: February 26, 2015

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important...
Cover of A Primer on Mapping Class Groups (PMS-49)
by Benson Farb, Dan Margalit
Language: English
Release Date: September 26, 2011

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving...
Cover of Knots and Primes

Knots and Primes

An Introduction to Arithmetic Topology

by Masanori Morishita
Language: English
Release Date: November 27, 2011

This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory.    Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields....
Cover of Topological Dimension and Dynamical Systems
by Michel Coornaert
Language: English
Release Date: June 20, 2015

Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin...
Cover of Geometry and Topology of Manifolds

Geometry and Topology of Manifolds

10th China-Japan Conference 2014

by
Language: English
Release Date: June 3, 2016

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among...
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