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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Atiyah-Singer invariant, torsion invariants, and group actions on spheres


Author: Donald E. Smith
Journal: Trans. Amer. Math. Soc. 277 (1983), 469-488
MSC: Primary 57S25; Secondary 55Q50
MathSciNet review: 694371
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Abstract: This paper deals with the classification of cyclic group actions on spheres using the Atiyah-Singer invariant and Reidemeister-type torsion. Our main tool is the computation of the group of relative homotopy triangulations of the product of a disk and a lens space. These results are applied to obtain lower bounds on the image of an equivariant $ J$-homomorphism.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0694371-3
PII: S 0002-9947(1983)0694371-3
Article copyright: © Copyright 1983 American Mathematical Society