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Actions of Finite Groups on R n+k with Fixed Set R k

Published online by Cambridge University Press:  20 November 2018

Ian Hambleton  and
Ib Madsen
Ian Hambleton
Affiliation:
McMaster University, Hamilton, Ontario
Ib Madsen
Affiliation:
Universitet sparken, 8000 Aarhus C, Denmark
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In this paper we study the existence problem for topological actions of finite groups on euclidean spaces R n+k which are free outside a fixed point set R k (embedded as a vector subspace). We refer to such an action as a semi-free action on (R n+k , R n ) and note that all our actions will be assumed orientation-preserving.

Suppose the finite group π acts semi-freely on (R n+k , R n ), then it acts freely on (R n+k – R n ) = S n–l × R k+1. Since this space is homotopy equivalent to S n–l, π will have periodic integral cohomology and n will be a multiple of the period. In fact the orbit space

is a finitely-dominated Poincaré complex of formal dimension n – 1 with π 1 W = π and as considered by Swan [41].

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 4 , 01 August 1986 , pp. 781 - 860
Copyright
Copyright © Canadian Mathematical Society 1986

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