= Cartan formula
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{wiki=Cartan_formula#Cartan_formula_in_algebraic_topology}
= Cartan formula
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{synonym}
The Cartan product formula says that total <Steenrod squares> and total <Steenrod reduced powers> preserve the <cup product>:
$$
\operatorname{Sq}^k(ab)=\sum_{i+j=k}\operatorname{Sq}^i(a)\operatorname{Sq}^j(b),
\qquad
P^k(ab)=\sum_{i+j=k}P^i(a)P^j(b).
$$
It is named after Henri Cartan and is distinct from <Cartan's magic formula> for the <Lie derivative of a differential form>, named after Élie Cartan.
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