Topology

In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130].

In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "e;Algebras and Orders"e; as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation.

The book is an introduction to the foundations of Mathematics.

The first comprehensive introduction to the powerful moment approach for solving global optimization problems.

Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition.

An asymmetric norm is a positive definite sublinear functional p on a real vector space X.

Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G.

This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory.

The following lecture notes correspond to a course taught for several years, first at the University of Paris-Nord (France) and then at the University of Bologna (Italy).

This book reviews recent results on low-dimensional quantumfield theories and their connection with quantum grouptheory and the theory of braided, balanced tensorcategories.

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.

This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example.

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications.

This proceedings presents the latest research materials done on group theory from geometrical viewpoint in particular Gromov's theory of hyperbolic groups, Coxeter groups, Tits buildings and actions on real trees.

Energy of knots is a theory that was introduced to create a "e;canonical configuration"e; of a knot - a beautiful knot which represents its knot type.

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.

Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research.

A-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of earlier works of Sugawara's homotopy characterization of H-spaces and loop spaces.

The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry.

This engaging, well-motivated textbook helps advanced undergraduate students to grasp core concepts and reveals applications in mathematics and beyond.

The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators.

This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three.

This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds.

This proceedings is a collection of articles on Topology and Teichmuller Spaces.

This book is a Festschrift for the 90th birthday of the physicist Pierre Noyes.

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.

The Four Corners of Mathematics: A Brief History, from Pythagoras to Perelman describes the historical development of the 'big ideas' in mathematics in an accessible and intuitive manner.

An authoritative introduction to the essential features of etale cohomologyA.

Accessible and pedagogical introduction to the theory of harmonic maps, covering recent results and applications.

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E.

A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.

Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics.

This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging).

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory.

A rapid route for graduate students and researchers to the frontiers of research in this evergreen subject, first published in 2005.

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics.

This comprehensive guide addresses key challenges at the intersection of data science, graph learning, and privacy preservation.

The main goal of the book is to present a proof of the following.

This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics.

This updated and revised edition of a widely acclaimed and successful text for undergraduates examines topology of recent compact surfaces through the development of simple ideas in plane geometry.

A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.

This volume is based on lectures given at the highly successful three-week Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for Mathematical Sciences in July 2010.