The Atiyah-Patodi-Singer Index Theorem
Книжки с доказательством
теоремы Атьи-Зингера об индексе:

Peter B. Gilkey, INVARIANCE THEORY, THE HEAT EQUATION,
AND THE ATIYAH-SINGER INDEX THEOREM
http://www.emis.de/monographs/gilkey/

Richard Melrose, The Atiyah-Patodi-Singer Index Theorem
http://www-math.mit.edu/~rbm/book.html

Nigel Higson
The local index formula in noncommutative geometry
http://www.math.psu.edu/higson/Papers/trieste.pdf

Привет