Construction of group actions on fourmanifolds
Author:
Allan L. Edmonds
Journal:
Trans. Amer. Math. Soc. 299 (1987), 155170
MSC:
Primary 57N13; Secondary 57N15, 57S17, 57S25
MathSciNet review:
869405
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Abstract: It is shown that any cyclic group of odd prime order acts on any closed, simply connected topological manifold, inducing the identity on integral homology. The action is locally linear except perhaps at one isolated fixed point. In the case of primes greater than three a more careful argument is used to show that the action can be constructed to be locally linear.
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 [S]
 E. Cappell and J. L. Shaneson, The codimension two placement problem and homology equivalent manifolds, Ann. of Math. (2) 99 (1974), 277348. MR 0339216 (49:3978)
 [A]
 L. Edmonds, Preliminary notes on finite group actions on fourmanifolds, unpublished notes, 1984.
 [M]
 H. Freedman, The topology of fourdimensional manifolds, J. Differential Geom. 17 (1982), 357453. MR 679066 (84b:57006)
 1.
 , The disk theorem for fourdimensional manifolds, Proc. Internat. Congr. Math., Warsaw, Poland, 1983, pp. 647663. MR 804721 (86m:57016)
 [M]
 J. Greenberg and J. R. Harper, Algebraic topology: a first course. Benjamin/Cummings, Reading, Mass., 1981. MR 643101 (83b:55001)
 [F]
 Hirzebruch, W. D. Neumann, and S. S. Koh, Differentiable manifolds and quadratic forms, Marcel Dekker, New York, 1971. MR 0341499 (49:6250)
 [F]
 Hirzebruch and D. Zagier, The AtiyahSinger index theorem and elementary number theory, Publish or Perish, Boston, 1973.
 [W]
 C. Hsiang and R. H. Szczarba, On embedding surfaces in fourmanifolds, Proc. Sympos. Pure Math., vol. 22, Amer. Math. Soc., Providence, R.I., 1971, pp. 97103. MR 0339239 (49:4000)
 [S]
 Kwasik, On symmetries of the fake , Preprint, 1985. MR 842620 (87h:57034)
 [S]
 Kwasik and P. Vogel, Asymmetric fourdimensional manifolds, Preprint, 1984. MR 860670 (88c:57038)
 2.
 , Nonlocally smoothable topological symmetries of four manifolds, Preprint, 1985.
 [J]
 W. Milnor, A duality theorem for Reidemeister torsion, Ann. of Math. (2) 76 (1962), 137147. MR 0141115 (25:4526)
 3.
 , Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358426. MR 0196736 (33:4922)
 [L]
 R. Taylor, Relative Rochlin invariant, Topology Appl. 18 (1984), 259280. MR 769295 (86g:57027)
 [C]
 T. C. Wall, Surgery on compact manifolds, Academic Press, London, 1970. MR 0431216 (55:4217)
 [S]
 H. Weintraub, Semifree actions on highlyconnected manifolds, Math. Z. 145 (1975), 163185. MR 0400268 (53:4103)
 4.
 , Topological realization of equivariant intersection forms, Pacific J. Math. 73 (1977), 257280. MR 0494175 (58:13100)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198708694057
PII:
S 00029947(1987)08694057
Article copyright:
© Copyright 1987
American Mathematical Society
