Higher torsion in the Morava \(K\)-theory of \(SO(m)\) and \(Spin(m)\). (English) Zbl 0983.55004

Nishimoto, Tetsu

J. Math. Soc. Japan 53, No. 2, 383-394 (2001).

This paper is a continuation of [J. Hunton, M. Mimura, T. Nishimoto and B. Schuster, ibid. 50, No. 4, 801-818 (1998; Zbl 0923.55004)]. The author determines the \(K(n)^*\)-module structure of the Morava \(K\)-theories \(K(n)^*(\text{SO}(m))\) and \(K(n)^* (\text{Spin}(m))\), for the special orthogonal groups and the spinor groups, at the prime 2. The main tool is the Atiyah-Hirzebruch spectral sequence.

Reviewer: Daniel Tanré (Villeneuve d’ Ascq)

MSC:

55N20	Generalized (extraordinary) homology and cohomology theories in algebraic topology
57T10	Homology and cohomology of Lie groups
55T25	Generalized cohomology and spectral sequences in algebraic topology

Keywords:

Atiyah-Hirzebruch spectral sequence

Citations:

Zbl 0923.55004