Difference between revisions of "Todd class"
From Encyclopedia of Mathematics
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$$\sum_{j=0}^\infty T_j(c_1,\dots,c_j),$$ | $$\sum_{j=0}^\infty T_j(c_1,\dots,c_j),$$ | ||
| − | where $\{T_j\}$ is the [[Todd polynomials]], defined by the [[multiplicative sequence]] corresponding to the [[power series]] $t/(1-e^{-t})$ and $c_i$ are the [[Chern class]]es. | + | 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 class]]es. |
Introduced by J. Todd [[#References|[1]]]. | Introduced by J. Todd [[#References|[1]]]. | ||
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====References==== | ====References==== | ||
<table> | <table> | ||
| − | <TR><TD valign="top">[1]</TD> <TD valign="top"> J. Todd, "The arithmetical theory of algebraic loci" ''Proc. London Math. Soc.'' , '''43''' (1937) pp. 190–225</TD></TR> | + | <TR><TD valign="top">[1]</TD> <TD valign="top"> J. Todd, "The arithmetical theory of algebraic loci" ''Proc. London Math. Soc.'' , '''43''' (1937) pp. 190–225 {{ZBL|63.0624.03}}</TD></TR> |
<TR><TD valign="top">[2]</TD> <TD valign="top"> F. Hirzebruch, "Topological methods in algebraic geometry" , Springer (1978) (Translated from German) {{MR|1335917}} {{MR|0202713}} {{ZBL|0376.14001}} </TD></TR> | <TR><TD valign="top">[2]</TD> <TD valign="top"> F. Hirzebruch, "Topological methods in algebraic geometry" , Springer (1978) (Translated from German) {{MR|1335917}} {{MR|0202713}} {{ZBL|0376.14001}} </TD></TR> | ||
</table> | </table> | ||
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====Comments==== | ====Comments==== | ||
Cf. [[Characteristic class|Characteristic class]] for the notion of a multiplicative sequence. | Cf. [[Characteristic class|Characteristic class]] for the notion of a multiplicative sequence. | ||
Latest revision as of 07:42, 18 March 2023
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].
References
| [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 |
Comments
Cf. Characteristic class for the notion of a multiplicative sequence.
How to Cite This Entry:
Todd class. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Todd_class&oldid=35550
Todd class. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Todd_class&oldid=35550
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article