 # Topology

## subcategories

Algebraic (37)
Differential (15)
Geometric (32)
Point-set (14)

## e-books in Topology category Topology
by - Harvard University ,
Contents: Introduction; Background in set theory; Topology; Connected spaces; Compact spaces; Metric spaces; Normal spaces; Algebraic topology and homotopy theory; Categories and paths; Path lifting and covering spaces; Global topology; etc.
(7332 views) Manifolds
by - King's College London ,
From the table of contents: Manifolds (Elementary Topology and Definitions); The Tangent Space; Maps Between Manifolds; Vector Fields; Tensors; Differential Forms; Connections, Curvature and Metrics; Riemannian Manifolds.
(9442 views) Exact Sequences in the Algebraic Theory of Surgery
by - Princeton University Press ,
One of the principal aims of surgery theory is to classify the homotopy types of manifolds using tools from algebra and topology. The algebraic approach is emphasized in this book, and it gives the reader a good overview of the subject.
(9307 views) Noncommutative Localization in Algebra and Topology
by - Cambridge University Press ,
Noncommutative localization is a technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. The applications to topology are via the noncommutative localizations of the fundamental group rings.
(8825 views) Lectures on Sheaf Theory
by - Tata Institute of Fundamental Research ,
A sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. Contents: Sheaves; Sections; Cohomology groups of a space with coefficients in a presheaf; Introduction of the family Phi; etc.
(9240 views) Special Course in Functional Analysis: (Non-)Commutative Topology
by - Aalto TKK ,
In this book you will learn something about functional analytic framework of topology. And you will get an access to more advanced literature on non-commutative geometry, a quite recent topic in mathematics and mathematical physics.
(10957 views) Lecture Notes on Seiberg-Witten Invariants
by - Springer ,
A streamlined introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure.
(9744 views) Topology and Physics: A Historical Essay
by - arXiv ,
In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
(13581 views) Floer Homology, Gauge Theory, and Low Dimensional Topology
by - American Mathematical Society ,
Mathematical gauge theory studies connections on principal bundles. The book provides an introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds.
(12758 views) Optimization Algorithms on Matrix Manifolds
by - Princeton University Press ,
Many science and engineering problems can be rephrased as optimization problems on matrix search spaces endowed with a manifold structure. This book shows how to exploit the structure of such problems to develop efficient numerical algorithms.
(17271 views) Manifolds and Differential Forms
by - Cornell University ,
The text covers manifolds and differential forms for an audience of undergraduates who have taken a typical calculus sequence, including basic linear algebra and multivariable calculus up to the integral theorems of Green, Gauss and Stokes.
(12330 views) The Convenient Setting of Global Analysis
by - American Mathematical Society ,
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory.
(12952 views)