## subcategories

**Algebraic** (37)

**Differential** (14)

**Geometric** (31)

**Point-set** (15)

## e-books in Topology category

**Topology**

by

**Curtis T. McMullen**-

**Harvard University**,

**2013**

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.

(

**2853**views)

**Manifolds**

by

**Neil Lambert**-

**King's College London**,

**2011**

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.

(

**5138**views)

**Exact Sequences in the Algebraic Theory of Surgery**

by

**Andrew Ranicki**-

**Princeton University Press**,

**1981**

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.

(

**5378**views)

**Noncommutative Localization in Algebra and Topology**

by

**Andrew Ranicki**-

**Cambridge University Press**,

**2002**

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.

(

**4738**views)

**Lectures on Sheaf Theory**

by

**C.H. Dowker**-

**Tata Institute of Fundamental Research**,

**1957**

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.

(

**5400**views)

**Special Course in Functional Analysis: (Non-)Commutative Topology**

by

**Ville Turunen**-

**Aalto TKK**,

**2008**

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.

(

**6535**views)

**Lecture Notes on Seiberg-Witten Invariants**

by

**John Douglas Moore**-

**Springer**,

**2010**

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.

(

**5558**views)

**Topology and Physics: A Historical Essay**

by

**C. Nash**-

**arXiv**,

**1997**

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.

(

**8487**views)

**Floer Homology, Gauge Theory, and Low Dimensional Topology**

by

**David Ellwood, at al.**-

**American Mathematical Society**,

**2006**

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.

(

**7833**views)

**Optimization Algorithms on Matrix Manifolds**

by

**P.-A. Absil, R. Mahony, R. Sepulchre**-

**Princeton University Press**,

**2007**

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.

(

**11767**views)

**Manifolds and Differential Forms**

by

**Reyer Sjamaar**-

**Cornell University**,

**2017**

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.

(

**7727**views)

**The Convenient Setting of Global Analysis**

by

**Andreas Kriegl, Peter W. Michor**-

**American Mathematical Society**,

**1997**

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.

(

**8709**views)