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Elliptic Operators, Topology, and Asymptotic Methods
John Roe
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Description for Elliptic Operators, Topology, and Asymptotic Methods
Paperback. 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. Series: Chapman & Hall/CRC Research Notes in Mathematics Series. Num Pages: 209 pages, black & white illustrations. BIC Classification: PBKJ; PBM; PBP. Category: (P) Professional & Vocational. Dimension: 233 x 157 x 12. Weight in Grams: 344.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
1999
Publisher
Pearson Education Limited United Kingdom
Number of pages
209
Condition
New
Series
Chapman & Hall/CRC Research Notes in Mathematics Series
Number of Pages
216
Place of Publication
Harlow, United Kingdom
ISBN
9780582325029
SKU
V9780582325029
Shipping Time
Usually ships in 4 to 8 working days
Ref
99-1
About John Roe
John Roe
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