Topology

This book presents a complete proof of Connes'' Index Theorem generalized to foliated spaces, including coverage of new developments and applications.

Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics.

Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.

Were I to take an iron gun, And ?

As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely.

In two volumes, this comprehensive treatment covers all that is needed to understand and appreciate this beautiful branch of mathematics.

Graph Theory is a branch of discrete mathematics.

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces.

Eine gleichermaßen aktuelle wie zusammenfassende Darstellung der wichtigsten Methoden zur Untersuchung der klassischen Gruppen fehlte bislang in deutschsprachigen Lehrbüchern.

These proceedings include selected and refereed original papers; most are research papers, a few are comprehensive survey articles.

Far from being separate entities, many social and engineering systems can be considered as complex network systems (CNSs) associated with closely linked interactions with neighbouring entities such as the Internet and power grids.

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces.

A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory.

This textbook provides a succinct introduction to algebraic topology.

This book is part of the series of three books arise from lectures organized by Hitoshi Murakami at RIMS, Kyoto University in the summer of 2001.

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory.

This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.

One service mathematics has rendered the human race.

Presenting the latest findings in topics from across the mathematical spectrum, this volume includes results in pure mathematics along with a range of new advances and novel applications to other fields such as probability, statistics, biology, and computer science.

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory.

A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems.

The leveraging of artificial intelligence (AI) for model discovery in dynamical systems is cross-fertilizing and revolutionizing both disciplines, heralding a new era of data-driven science.

Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results.

'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 aim of this book is to present recently discovered connections between Artin's braid groups En and left self-distributive systems (also called LD- systems), which are sets equipped with a binary operation satisfying the left self-distributivity identity x(yz) = (xy)(xz).

A self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory.

This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis.

This book serves as a textbook in real analysis.

Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points.

This book is essential reading for anyone interested in low-dimensional topology.

The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade.

This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018.

About one and a half decades ago, Feigenbaum observed that bifurcations, from simple dynamics to complicated ones, in a family of folding mappings like quadratic polynomials follow a universal rule (Coullet and Tresser did some similar observation independently).

This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications.

The Standard Model is the foundation of modern particle and high energy physics.

The volume consists of a set of surveys on geometry in the broad sense.

In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group theory.

This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification.

The book, based on the INdAM Workshop "e;Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology"e; provides a bridge between different communities of mathematicians who utilize splines in their work.