Abstract
The notions of simple homotopy theory and Whitehead torsion have generalizations in the theory of transformation groups. One does not have to consider free actions. A geometric description of a generalized Whitehead group was given by Illman. The approach resembles that of Cohen. An algebraic approach was pursued by Rothenberg. This approach has been developed only under certain assumptions. In this paper we generalize the approach to give an algebraic description of the generalized Whitehead group for a finite group. In particular we put no restrictions on the component structure of the action and we do not assume that H fixed point components are 1-connected. We prove that our and Illman's approach lead to the same group.
Partially supported by NSF Grant MCS 8100751 and 8514551
Partially supported by NSF Grant MCS 7701623
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© 1986 Springer-Verlag
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Dovermann, K.H., Rothenberg, M. (1986). An algebraic approach to the generalized Whitehead group. In: Jackowski, S., Pawałowski, K. (eds) Transformation Groups Poznań 1985. Lecture Notes in Mathematics, vol 1217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072817
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DOI: https://doi.org/10.1007/BFb0072817
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