High Quality Content by WIKIPEDIA articles! In mathematics, in
particular in partial differential equations and differential
geometry, an elliptic complex generalizes the notion of an elliptic
operator to sequences. Elliptic complexes isolate those features
common to the de Rham complex and the Dolbeault complex which are
essential for performing Hodge theory. They also arise in
connection with the Atiyah-Singer index theorem and Atiyah-Bott
fixed point theorem.