Algebraic topology

Rational homotopy is a very powerful tool for differential topology and geometry.

This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds.

Fibre bundles play an important role in just about every aspect of modern geometry and topology.

In recent years, there has been increasing interest and activity in the area of group actions on affine and projective algebraic varieties.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

This book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.

This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role.

The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology.

The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics.

This Volume presents a unified approach to calculate the plane stress distribution of stress and strain in thin elastic/plastic discs subject to various loading conditions.

Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.

This monograph summarizes and extends a number of results on the topology of trigonal curves in geometrically ruled surfaces.

This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics.

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds.

An elementary introduction to homology theory suitable for undergraduate courses or for self-study.

A NATO Advanced Study Institute entitled "e;Algebraic K-theory and Algebraic Topology"e; was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991.

Any topological theory of knots and links should be based on simple ideas of intersection and linking.

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

An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.

Fields-medal winner Donaldson reviews current work, including his own, on the theory of Floer.

Etale Cohomology is one of the most important methods in modern Algebraic Geometry and Number Theory.

This volume includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths.

This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought.

This monograph provides a comprehensive treatment of the classification of small fusion systems, that is, fusion systems with few essential subgroups.

Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems.

With one exception, these papers are original and fullyrefereed research articles on various applications ofCategory Theory to Algebraic Topology, Logic and ComputerScience.

Real analytic sets in Euclidean space (Le.

This book provides a definition of Green functors for a finite group G, and of modules over it, in terms of the category of finite G-sets.

The first book to give a complete treatment of rigid cohomology, from the basics to the very latest developments.

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 textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout.

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

This is an in-depth report on the endotrivial modules, an important class of modular representations for finite groups.

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

Providing a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the product structure in a geometric manner.

Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form.

Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V.

Differential and complex geometry are two central areas of mathematics with a long and intertwined history.

This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community.

A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.

The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact.

This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent.

Introduction In the present essay, we attempt to convey some idea of the skeleton of topology, and of various topological concepts.

This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA).

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

This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.