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geometry > differential geometry > Atiyah-Singer index theorem
mathematical physics > differential operator > Atiyah-Singer index theorem
mathematical analysis > functional analysis > operator > differential operator > Atiyah-Singer index theorem
... > mathematical analysis > equation > functional equation > differential equation > partial differential equation > elliptic partial differential equation > Atiyah-Singer index theorem
... > mathematical analysis > calculus > differential calculus > differential equation > partial differential equation > elliptic partial differential equation > Atiyah-Singer index theorem

Preferred term

Atiyah-Singer index theorem  

Definition(s)

  • In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data). It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer_index_theorem)

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RDF/XML TURTLE JSON-LD Created 7/19/23, last modified 8/22/23