Chromatic structures in stable homotopy theory

Authored by: Tobias Barthel , Agnès Beaudry

Handbook of Homotopy Theory

Print publication date:  December  2019
Online publication date:  December  2019

Print ISBN: 9780815369707
eBook ISBN: 9781351251624
Adobe ISBN:


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At its core, chromatic homotopy theory provides a natural approach to the computation of the stable homotopy groups of spheres π ∗ S 0 . Historically, the first few of these groups were computed geometrically through the classification of stably framed manifolds, using the Pontryagin–Thom isomorphism π ∗ S 0 ≅ Ω ∗ fr . However, beginning with the work of Serre, it soon turned out that algebraic tools were more effective, both for the computation of specific low-degree values as well as for establishing structural results. In particular, Serre proved that π ∗ S 0 is a degreewise finitely generated abelian group with π 0 S 0 ≅ Z and that all higher groups are torsion.

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