Elliptic operators, topology and asymptotic methods

The index theorem is a central result of modern mathematics and all students of global analysis need to be familiar with it. This edition preserves the brevity of the first edition, but includes new material and reworkings of some of the more difficult arguments. This Research Note gives an introduction to the circle of ideas surrounding the `heat equation proof' of the Atiyah-Singer index theorem. Asymptotic expansions for the solutions of partial differential equations on compact manifolds are used to obtain topological information, by means of a `supersymmetric' cancellation of eigenspaces. The analysis is worked out in the context of Dirac operators on Clifford bundles.

The work includes proofs of the Hodge theorem; eigenvalue estimates; the Lefschetz theorem; the index theorem; and the Morse inequalities. Examples illustrate the general theory, and several recent results are included.

This new edition has been revised to streamline some of the analysis and to give better coverage of important examples and applications.

Readership: The book is aimed at researchers and graduate students with a background in differential geometry and functional analysis.

UK Delivery:

• Free delivery on all orders of £10 or more.
• £1.49 delivery fee on orders below £10.
• UK orders are shipped via Royal Mail 2nd Class.

International Delivery:

• Flat rate delivery charges vary by country.

Dispatch and Delivery Times:

• All orders are shipped from our warehouse in Northampton, UK within 48 hours of receipt during working hours.
• UK mainland orders typically arrive within 3-5 working days via Royal Mail 2nd Class.
• International estimated delivery times:
• Europe & Channel Islands: 7 to 10 working days
• USA: 7 to 15 working days
• Rest of the World: 9 to 21 working days

View our full delivery infomation here.