Editing Bernoulli number (section)

=== Use in topology ===
The [[Kervaire–Milnor formula]] for the order of the cyclic group of diffeomorphism classes of [[exotic sphere|exotic {{math|(4''n'' − 1)}}-spheres]] which bound [[parallelizable manifold]]s involves Bernoulli numbers. Let {{math|''ES''<sub>''n''</sub>}} be the number of such exotic spheres for {{Math|''n'' ≥ 2}}, then

:<math>\textit{ES}_n = (2^{2n-2}-2^{4n-3}) \operatorname{Numerator}\left(\frac{B_{4n}}{4n} \right) .</math>

The [[Hirzebruch signature theorem#L genus and the Hirzebruch signature theorem|Hirzebruch signature theorem]] for the [[Hirzebruch signature theorem#L genus and the Hirzebruch signature theorem|{{mvar|L}} genus]] of a [[Smooth manifold|smooth]] [[Orientability|oriented]] [[closed manifold]] of [[dimension]] 4''n'' also involves Bernoulli numbers.