subcategories
Algebraic (37)
Differential (15)
Geometric (32)
Point-set (14)
e-books in Topology category
Topologyby 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.
(8180 views)
Manifoldsby 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.
(10213 views)
Exact Sequences in the Algebraic Theory of Surgeryby 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.
(10133 views)
Noncommutative Localization in Algebra and Topologyby 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.
(9680 views)
Lectures on Sheaf Theoryby 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.
(10306 views)
Special Course in Functional Analysis: (Non-)Commutative Topologyby 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.
(11809 views)
Lecture Notes on Seiberg-Witten Invariantsby 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.
(10636 views)
Topology and Physics: A Historical Essayby 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.
(14486 views)
Floer Homology, Gauge Theory, and Low Dimensional Topologyby 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.
(13747 views)
Optimization Algorithms on Matrix Manifoldsby 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.
(18268 views)
Manifolds and Differential Formsby 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.
(13329 views)
The Convenient Setting of Global Analysisby 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.
(13892 views)