subcategories
Algebraic (37)
Differential (15)
Geometric (32)
Point-set (14)
e-books in Topology category
![Book cover: Topology](images/9780.jpg)
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.
(8096 views)
![Book cover: Manifolds](images/8704.jpg)
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.
(10144 views)
![Book cover: Exact Sequences in the Algebraic Theory of Surgery](images/6986.jpg)
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.
(10042 views)
![Book cover: Noncommutative Localization in Algebra and Topology](images/6961.jpg)
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.
(9588 views)
![Book cover: Lectures on Sheaf Theory](images/6146.jpg)
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.
(10160 views)
![Book cover: Special Course in Functional Analysis: (Non-)Commutative Topology](images/blank.gif)
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.
(11730 views)
![Book cover: Lecture Notes on Seiberg-Witten Invariants](images/5670.jpg)
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.
(10532 views)
![Book cover: Topology and Physics: A Historical Essay](images/5500.jpg)
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.
(14386 views)
![Book cover: Floer Homology, Gauge Theory, and Low Dimensional Topology](images/5220.jpg)
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.
(13655 views)
![Book cover: Optimization Algorithms on Matrix Manifolds](images/2523.jpg)
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.
(18174 views)
![Book cover: Manifolds and Differential Forms](images/2493.jpg)
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.
(13225 views)
![Book cover: The Convenient Setting of Global Analysis](images/2199.jpg)
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.
(13795 views)