Topology Books

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems,...

These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to...

Matrix Groups.- Concrete Matrix Groups. The Matrix Exponential Function. Linear Lie Groups. Lie Algebras.- Elementary Structure Theory of Lie Algebras. Root Decomposition. Representation Theory of Lie Algebras.

A new combinatorial foundation of the two concepts, based on a consideration of deep and classical results of homotopy theory, and an axiomatic characterization of the assumptions under which results in this field hold...

Homotopy is a basic discipline of mathematics having fundamental and various applications to important fields of mathematics. The Journal has a wide scope which ranges from homotopical algebra and algebraic number theory and functional analysis. Diverse...

1 History.- 2 (Topological) Maps.- 3 The Four-Color Theorem (Topological Version).- 4 Topology to Combinatorics.- 5 The Four-Color Theorem (Combinatorial Version).- 6 Reducibility.- 7 The Quest for Unavoidable Sets.- Works of Reference.

Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of...

Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have as- sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics. The three...

Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings. This book deals with the topology of curves...

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but...

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and...

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core...

Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics...

''Intended mainly for physicists and mathematicians...its high quality will definitely attract a wider audience.'' ---Computational Mathematics and Mathematical Physics This work acquaints the physicist with the...

This book is a groundbreaking work in the field of topology, exploring the properties of homotopy spheres and the various groups that can be derived from them. With detailed proofs and rigorous analysis, this book is a must-read for anyone interested in...

Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of...