Editing Todd class (section)

In [[mathematics]], the '''Todd class''' is a certain construction now considered a part of the theory in [[algebraic topology]] of [[characteristic class]]es.  The Todd class of a [[vector bundle]] can be defined by means of the theory of [[Chern class]]es, and is encountered where Chern classes exist &mdash; most notably in [[differential topology]], the theory of [[complex manifold]]s 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 the [[Grothendieck–Riemann–Roch theorem|Grothendieck–Hirzebruch–Riemann–Roch theorem]].