Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classically in the Gauss-Bonnet theorem and its generalizations. which culminate in the Atiyah-Singer Index Theorem [AS1] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topological properties of the manifold.
KeywordsElliptic Operator Pseudodifferential Operator Topological Index Index Theorem Chern Character
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