nLab Samelson product

Idea

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Related concepts

• Whitehead product

• Pontrjagin product

References

Original reference, proving that the Whitehead product is the commutator of the Pontrjagin product:

• Hans Samelson, A Connection Between the Whitehead and the Pontryagin Product, American Journal of Mathematics 75 4 (1953) 744–752 [doi:10.2307/2372549]

Expository accounts:

• Joseph Neisendorfer, Samelson products and exponents of homotopy groups, Journal of Homotopy and Related Structures 8:2 (2013), 239-277 doi:10.1007/s40062-012-0021-4.

• Joseph Neisendorfer. Samelson products, Chapter 6 in: Algebraic Methods in Unstable Homotopy Theory, 158-220. Cambridge University Press. doi:10.1017/cbo9780511691638.008.

History:

• Ioan Mackenzie James, Products between homotopy groups, Compositio Mathematica, 23 3 (1971) , 329-345 [numdam:CM_1971__23_3_329_0]