In mathematics, the Todd class is a certain construction now considered a part of the theory in algebraic topology of characteristic classes. The Todd class of a vector bundle can be defined by means of the theory of Chern classes, and is encountered where Chern classes exist — most notably in differential topology, the theory of complex manifolds and algebraic geometry. In rough terms, a Todd class acts like a reciprocal of a Chern class, or stands in relation to it as a conormal bundle does to a normal bundle.
The Todd class plays a fundamental role in generalising the classical Riemann-Roch theorem to higher dimensions, in the Hirzebruch-Riemann-Roch theorem and Grothendieck-Hirzebruch-Riemann-Roch theorem.
Read more about Todd Class: History, Definition, Properties of Todd Class, Hirzebruch-Riemann-Roch Formula
Famous quotes containing the words todd and/or class:
“You dont have power if you surrender all your principlesyou have office.”
—Ron Todd (b. 1927)
“The class at Harvard in 1851, have purchased for themselves a notoriety they will not covet in years to come.”
—Harriot K. Hunt (18051875)