Abelian -group actions on homology spheres

Author:
Ronald M. Dotzel

Journal:
Proc. Amer. Math. Soc. **83** (1981), 163-166

MSC:
Primary 57S17; Secondary 55M35

DOI:
https://doi.org/10.1090/S0002-9939-1981-0620005-3

MathSciNet review:
620005

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Abstract: The Borel formula is extended to an identity covering actions of arbitrary Abelian -groups. Specifically, suppose is an Abelian -group which acts on a finite -complex which is a -homology -sphere. Each must be a -homology -sphere and then

This result is an immediate corollary of Theorem 2, whose converse Theorem 1, is also proven. Thus actions of Abelian -groups on homology spheres resemble linear representations.

**[1]**A. Borel,*Seminar on transformation groups*, Ann. of Math. Studies, no. 46, Princeton Univ. Press, Princeton, N.J., 1960. MR**0116341 (22:7129)****[2]**G. Bredon,*Introduction to compact transformation groups*, Academic Press, New York, 1972. MR**0413144 (54:1265)****[3]**-,*Equivariant cohomology theories*, Lecture Notes in Math., vol. 34, Springer-Verlag, Berlin and New York, 1967. MR**0214062 (35:4914)****[4]**R. Dotzel,*A converse to the Borel formula*, Trans. Amer. Math. Soc.**250**(1979), 275-287. MR**530056 (80g:55004)****[5]**-,*A note on the Borel formula*, Proc. Amer. Math. Soc.**78**(1980), 585-589. MR**556637 (81c:55004)**

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0620005-3

Article copyright:
© Copyright 1981
American Mathematical Society