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Difference between revisions of "Todd class"

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A [[Characteristic class|characteristic class]] of a complex bundle <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092930/t0929301.png" />, equal to
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{{TEX|done}}{{MSC|57R20}}
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092930/t0929302.png" /></td> </tr></table>
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A [[characteristic class]] of a complex bundle $\zeta$, equal to
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092930/t0929303.png" /> is the multiplicative sequence corresponding to the power series <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092930/t0929304.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092930/t0929305.png" /> are the Chern classes (cf. [[Chern class|Chern class]]).
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$$\sum_{j=0}^\infty T_j(c_1,\dots,c_j),$$
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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]]].
  
 
====References====
 
====References====
<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">[2]</TD> <TD valign="top"> F. Hirzebruch,   "Topological methods in algebraic geometry" , Springer (1978) (Translated from German)</TD></TR></table>
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<table>
 
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<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>
 
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<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>
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</table>
  
 
====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=11395
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article