by Curtis T. McMullen
Publisher: Harvard University 2013
Number of pages: 90
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: applications; Quotients, gluing and simplicial complexes; Galois theory of covering spaces; Free groups and graphs; Group presentations, amalgamation and gluing.
Home page url
Download or read it online for free here:
by Andrew Ranicki - 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.
by Neil Lambert - 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.
by C.H. Dowker - 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.
by Andreas Kriegl, Peter W. Michor - 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.