Atiyah-Singer index theorem

proper noun

A theorem stating 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).

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

proper noun
  1. differential geometryA theorem stating 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).

Origin

Proved by Michael Atiyah and Isadore Singer in 1963.

Full word history & related roots →
Cite this entry
APA

Atiyah-Singer index theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/Atiyah-Singer%20index%20theorem

MLA

“Atiyah-Singer index theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Atiyah-Singer%20index%20theorem. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “Atiyah-Singer index theorem,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/Atiyah-Singer%20index%20theorem.

Source: Atiyah-Singer index theorem on Wiktionary, CC BY-SA 4.0.