Todd class

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2020 Mathematics Subject Classification: Primary: 57R20 [MSN][ZBL]

A characteristic class of a complex bundle $\zeta$, equal to

$$\sum_{j=0}^\infty T_j(c_1,\dots,c_j),$$

where $\{T_j\}$ is the sequence of Todd polynomials, defined by the multiplicative sequence corresponding to the power series $t/(1-e^{-t})$ and $c_i$ are the Chern classes.

Introduced by J. Todd [1].


[1] J. Todd, "The arithmetical theory of algebraic loci" Proc. London Math. Soc. , 43 (1937) pp. 190–225 Zbl 63.0624.03
[2] F. Hirzebruch, "Topological methods in algebraic geometry" , Springer (1978) (Translated from German) MR1335917 MR0202713 Zbl 0376.14001


Cf. Characteristic class for the notion of a multiplicative sequence.

How to Cite This Entry:
Todd class. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article