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The stable signature of a regular cyclic action

Author: Robert D. Little
Journal: Proc. Amer. Math. Soc. 130 (2002), 259-266
MSC (2000): Primary 57S17
Published electronically: July 31, 2001
MathSciNet review: 1855644
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Abstract: Let $p$ be an odd prime and $g: M^{2n}\longrightarrow M^{2n}$ a smooth map of order $p$. Suppose that the cyclic action defined by $g$ is regular and has fixed point set $F$. If the $g$-signature Sign$(g, M)$ is a rational integer and $n<p-1$, then there exists a choice of orientations such that Sign$(g, M)=$ Sign $F$.

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  • 1. J. P. Alexander, G. C. Hamrick and J. W. Vick, The signature of the fixed set of odd period, Proc. Amer. Math. Soc. 57 (1976), 327-331. MR 53:11632
  • 2. M. F. Atiyah and I. M. Singer, The index of elliptic operators, III, Ann. of Math. 87 (1968), 546-604. MR 38:5245
  • 3. D. Berend and G. Katz, Separating topology and number theory in the Atiyah-Singer $g$-signature formula, Duke Math. J. 61 (1990), 939-971. MR 91k:58122
  • 4. K. H. Dovermann and R. D. Little, Cohomology complex projective space with degree one codimension-two fixed submanifolds, Pacific J. Math. 173 (1996), 197-211. MR 97f:57039
  • 5. F. Hirzebruch and D. Zagier, The Atiyah-Singer Theorem and Elementary Number Theory, Mathematics Lecture Series No. 3 (1974), Publish or Perish, Boston. MR 58:31291
  • 6. K. Kawakubo, The index and the generalized Todd genus of $\mathbb Z _{p}$ actions, Amer. J. Math. 97 (1975), 182-204. MR 51:14118
  • 7. R. D. Little, Self-intersection of fixed manifolds and relations for the multisignature, Math. Scand. 69 (1991), 167-178. MR 93a:57030
  • 8. D. C. Royster, An analogue of the stabilization map for regular $\mathbb Z_{p}$ actions, Rocky Mountain J. Math. 24 (1994), 689-708. MR 95h:57044
  • 9. C. T. C. Wall, Surgery on Compact Manifolds, Academic Press, London (1970). MR 55:4217

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Additional Information

Robert D. Little
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822-2330

Received by editor(s): May 19, 2000
Published electronically: July 31, 2001
Communicated by: Ralph Cohen
Article copyright: © Copyright 2001 American Mathematical Society

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