Atiyah-Singer Index Theorem

A theorem which states that the analytic and topological ``indices'' are equal for any elliptic differential operator on an $n$-D Compact Differentiable $\Bbb{C}^\infty$ boundaryless Manifold.

See also Compact Manifold, Differentiable Manifold

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.

Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, p. 4, 1996.