Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.

part |1 pages

Introduction and the proof

chapter 1|2 pages

The Atiyah-Singer index theorem

chapter 3|1 pages

Boundary conditions versus b-geometry

chapter 4|4 pages

Preliminaries to the proof

chapter 5|1 pages

The proof

chapter 6|2 pages


chapter 7|3 pages


chapter 1|10 pages

Ordinary differential operators

chapter 2|42 pages

Exact b-geometry

chapter 3|28 pages

Spin structures

chapter 4|49 pages

Small b-calculus

chapter 5|64 pages

Full calculus

chapter 6|44 pages

Relative index, cohomology and resolvent

chapter 7|43 pages

Heat calculus

chapter 8|48 pages

Local index theorem

chapter 9|21 pages

Proof revisited and applications