TOPICS
Search

Atiyah-Singer Index Theorem


A theorem which states that the analytic and topological "indices" are equal for any elliptic differential operator on an n-dimensional compact smooth C^infty boundaryless manifold.

For their discovery and proof is this theorem, Atiyah and Singer shared the 2004 Abel prize.


See also

Compact Manifold, Smooth Manifold

Explore with Wolfram|Alpha

References

Atiyah, M. F. and Singer, I. M. "The Index of Elliptic Operators on Compact Manifolds." Bull. Amer. Math. Soc. 69, 322-433, 1963.Atiyah, M. F. and Singer, I. M. "The Index of Elliptic Operators I, II, III." Ann. Math. 87, 484-604, 1968.Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, p. 4, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.Rognes, J. "On the Atiyah-Singer Index Theorem." http://www.abelprisen.no/nedlastning/2004/popular_english_2004.pdf.

Referenced on Wolfram|Alpha

Atiyah-Singer Index Theorem

Cite this as:

Weisstein, Eric W. "Atiyah-Singer Index Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Atiyah-SingerIndexTheorem.html

Subject classifications