-invariants and finite covers. II

Author:
Larry Smith

Journal:
Trans. Amer. Math. Soc. **347** (1995), 5009-5021

MSC:
Primary 57R20; Secondary 55P42, 55Q45, 57M10

DOI:
https://doi.org/10.1090/S0002-9947-1995-1316862-2

MathSciNet review:
1316862

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Abstract: Let be a finite covering of closed framed manifolds. By the Pontrijagin-Thom construction both and define elements in the stable homotopy ring of spheres . Associated to and are their invariants , . If is a finite covering of closed oriented manifolds, then there is a related invariant of the diffeomorphism class of the covering. In a previous paper we examined the relation between these invariants. We reduced the determination of , as well as , for a -fold cover, to the evaluation of certain sums of roots of unity. In this sequel we show how the invariant theory of the cyclic group may be used to evaluate these rums. For example we obtain

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DOI:
https://doi.org/10.1090/S0002-9947-1995-1316862-2

Article copyright:
© Copyright 1995
American Mathematical Society