Topology

Differential Geometry and Its Visualization is suitable for graduate level courses in differential geometry, serving both students and teachers.

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

This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids.

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology.

This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds.

Combining theoretical and practical aspects of topology, this book provides a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data.

The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry.

This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning.

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis.

This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples.

The book addresses the minimization of special lower semicontinuous functionals over closed balls in metric spaces, called the approximate variation.

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).

Graduate students and researchers in applied mathematics, optimization, engineering,  computer science, and  management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization.

This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications.

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties.

The contributions in this volume-dedicated to the work and mathematical interests of Oleg Viro on the occasion of his 60th birthday-are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap among analysis, geometry, and topology.

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights.

How a simple equation reshaped mathematicsLeonhard 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.

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory.

In this book we study function spaces of low Borel complexity.

The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory.

This unique book offers an introductory course on category theory, which became a working language in algebraic geometry and number theory in the 1950s and began to spread to logic and computer science soon after it was created.

This book presents material in two parts.

The term "e;stereotype space"e; was introduced in 1995 and denotes a category of locally convex spaces with surprisingly elegant properties.

This book is ideal as an introduction to algebraic topology and applied algebraic topology featuring a streamlined approach including coverage of basic categorical notions, simplicial, cellular, and singular homology, persistent homology, cohomology groups, cup products, Poincare Duality, homotopy theory, and spectral sequences.

The term "e;stereotype space"e; was introduced in 1995 and denotes a category of locally convex spaces with surprisingly elegant properties.

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

This work covers quantum mechanics by answering questions such as where did the Planck constant and Heisenberg algebra come from, what motivated Feynman to introduce his path integral and why does one distinguish two types of particles, the bosons and fermions.

This work covers quantum mechanics by answering questions such as where did the Planck constant and Heisenberg algebra come from, what motivated Feynman to introduce his path integral and why does one distinguish two types of particles, the bosons and fermions.

The study of triangulations of topological spaces has always been at the root of geometric topology.

This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds.

This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary.

The book explains concepts and ideas of mathematics and physics that are relevant for advanced students and researchers of condensed matter physics.

The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry.

Etale cohomology is an important branch in arithmetic geometry.

This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article.

This conference brought together physicists and mathematicians working on spinors, which have played an important role in recent research on supersymmetry, Kaluza-Klein theories, twistors and general relativity.

This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology.

This book is about new topological invariants of real- and angle-valued maps inspired by Morse-Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics.

A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized.

This textbook is an alternative to a classical introductory book in point-set topology.

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.

After the positive settlement of Bieberbach's conjecture by Prof.

Over the last two decades, topological ideas have found increasingly more applications in quantum field theory.

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