Atiyah-Singer index theorem
Teorema del índice de Atiyah-Singer
- Date
- 1963 · confidence high
- Place
- Oxford and Cambridge, Massachusetts
- Credited to
- Michael Atiyah and Isadore Singer
- People
- 👤 Isadore Singer1924–2021👤 Michael Atiyah1929–2019
- Field
- Knowledge & symbols
What was discovered
The analytic index of an elliptic differential operator on a manifold (the dimension of solutions minus codimension) coincides with a topological invariant. It unites analysis, topology and geometry and generalises Gauss-Bonnet and Riemann-Roch.
Considered the most important theorem of 20th-century global geometry; Abel Prize 2004.
What it led to
- K-theory
- gauge theory and mathematical physics
- Donaldson and Seiberg-Witten invariants
- non-commutative geometry
Built on
- Gauss–Bonnet theorem1848
- Riemann–Roch theorem1857-1865
- Hirzebruch's theorem