Special Course in Functional Analysis: (Non-)Commutative Topology
by Ville Turunen
Publisher: Aalto TKK 2008
Number of pages: 83
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. The prerequisite for this course is some elementary understanding of Banach spaces.
Download or read it online for free here:
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.
by David Ellwood, at al. - 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.
by Andrew Ranicki - 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.
by Reyer Sjamaar - 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.