# Homotopy groups of spheres

## Idea

The homotopy groups of spheres

The stable homotopy groups of the sphere spectrum

## Tables

The first stable homotopy groups of the sphere spectrum $𝕊$

$k=$0123456789101112131415$\cdots$
${\pi }_{k}\left(𝕊\right)=$$ℤ$${ℤ}_{2}$${ℤ}_{2}$${ℤ}_{24}$$0$$0$${ℤ}_{2}$${ℤ}_{240}$$\left({ℤ}_{2}{\right)}^{2}$$\left({ℤ}_{2}{\right)}^{3}$${ℤ}_{6}$${ℤ}_{504}$$0$${ℤ}_{3}$$\left({ℤ}_{2}{\right)}^{2}$${ℤ}_{480}\oplus {ℤ}_{2}$

## References

• Alex Writght, Homotopy groups of spheres: A very basic introduction (pdf)

• Doug Ravenal, Complex cobordism and stable homotopy groups of spheres (web)

• Wikipedia, Homotopy groups of spheres

For formalization in homotopy type theory see at

Revised on May 8, 2013 03:48:12 by Toby Bartels (64.89.53.36)