Topology 1

This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and ……続きを見る

The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This ……続きを見る

"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, ……続きを見る

A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set top……続きを見る

The best-selling guide to network science, the revolutionary field that reveals the deep links between all forms of human social life A cocktail party. A terrorist cell. Ancient bacteria. An interna……続きを見る

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 20……続きを見る

This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link……続きを見る

This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in……続きを見る

The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks: - Geometry and topology of fibre bundles, - Cliff……続きを見る

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……続きを見る

K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts……続きを見る

Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topolo……続きを見る

In its simplest form, Hodge theory is the study of periods – integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized a……続きを見る

A classical theorem of Jordan states that every finite transitive permutation group contains a derangement. This existence result has interesting and unexpected applications in many areas of mathema……続きを見る

Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It c……続きを見る

Contemporary research in algebraic geometry is the focus of this collection, which presents articles on modern aspects of the subject. The list of topics covered is a roll-call of some of the most i……続きを見る

Few books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field……続きを見る

Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wile……続きを見る

Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wile……続きを見る

This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of ……続きを見る

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to ……続きを見る

Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading e……続きを見る

Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence t……続きを見る

This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presen……続きを見る

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generat……続きを見る

Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhed……続きを見る

This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, including in multi-graded situations, and provides……続きを見る

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 scie……続きを見る

This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinc……続きを見る

This text is an introduction to some of the mathematical wonders of Maxwell's equations. These equations led to the prediction of radio waves, the realization that light is a type of electromagnetic……続きを見る