# Computing v_1-periodic homotopy groups of spheres and some compact Lie
groups

## Donald M. Davis

To appear in Handbook of Algebraic Topology, Elsevier. Last updated mid-1994.
### Abstract

This survey paper includes the following topics:
- Definition of v_1-periodic homotopy groups.
- Reduction of unstable homotopy calculation to stable homotopy calculation.
- How to compute J-homology.
- Isomorphism of v_1-periodic stable homotopy with J-homology.
- v_1-periodic unstable Novikov spectral sequence for spheres.
- v_1-periodic homotopy groups of SU(n).
- v_1-periodic homotopy gorups of some Lie groups.

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