**The Convenient Setting of Global Analysis**

by Andreas Kriegl, Peter W. Michor

**Publisher**: American Mathematical Society 1997**ISBN/ASIN**: 0821807803**ISBN-13**: 9780821807804**Number of pages**: 624

**Description**:

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. Many applications are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.

Download or read it online for free here:

**Download link**

(4MB, PDF)

## Similar books

**An introductory course in differential geometry and the Atiyah-Singer index theorem**

by

**Paul Loya**-

**Binghamton University**

This is a lecture-based class on the Atiyah-Singer index theorem, proved in the 60's by Sir Michael Atiyah and Isadore Singer. Their work on this theorem lead to a joint Abel prize in 2004. Requirements: Knowledge of topology and manifolds.

(

**7139**views)

**Natural Operations in Differential Geometry**

by

**Ivan Kolar, Peter W. Michor, Jan Slovak**-

**Springer**

A comprehensive textbook on all basic structures from the theory of jets. It begins with an introduction to differential geometry. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces.

(

**11597**views)

**Synthetic Differential Geometry**

by

**Anders Kock**-

**Cambridge University Press**

Synthetic differential geometry is a method of reasoning in differential geometry and calculus. This book is the second edition of Anders Kock's classical text, many notes have been included commenting on new developments.

(

**8662**views)

**Notes on the Atiyah-Singer Index Theorem**

by

**Liviu I. Nicolaescu**-

**University of Notre Dame**

This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.

(

**5863**views)