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

Smith, Donald E.

doi:10.1090/S0002-9947-1983-0694371-3

The Atiyah-Singer invariant, torsion invariants, and group actions on spheres
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by Donald E. Smith

Trans. Amer. Math. Soc. 277 (1983), 469-488

DOI: https://doi.org/10.1090/S0002-9947-1983-0694371-3

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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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