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The involution on the equivariant Whitehead group. (English) Zbl 0685.57012

Let G be a finite group. The authors study the involution on the equivariant Whitehead group of a smooth G manifold induced by reversing the direction of an equivariant h-cobordism. This involution does not preserve the splitting into nonequivariant Whitehead groups, but is shown to do so when G has odd order. The authors use the involution to compute the Whitehead torsion of (f,\(\partial f): (M,\partial M)\to (N,\partial N)\) from that of f: \(M\to N\).
Reviewer: R.E.Stong

MSC:

57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57S17 Finite transformation groups
57R67 Surgery obstructions, Wall groups
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