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 | References | Similar Articles | Additional Information

Abstract: Let be an odd prime and a smooth map of order . Suppose that the cyclic action defined by is regular and has fixed point set . If the -signature Sign is a rational integer and , then there exists a choice of orientations such that Sign Sign .

**1.**J. P. Alexander, G. C. Hamrick, and J. W. Vick,*The signature of the fixed set of a map of odd period*, Proc. Amer. Math. Soc.**57**(1976), no. 2, 327–331. MR**0407862**, 10.1090/S0002-9939-1976-0407862-9**2.**M. F. Atiyah and I. M. Singer,*The index of elliptic operators. III*, Ann. of Math. (2)**87**(1968), 546–604. MR**0236952****3.**Daniel Berend and Gabriel Katz,*Separating topology and number theory in the Atiyah-Singer 𝑔-signature formula*, Duke Math. J.**61**(1990), no. 3, 939–971. MR**1084466**, 10.1215/S0012-7094-90-06136-8**4.**Karl H. Dovermann and Robert D. Little,*Cohomology complex projective space with degree one codimension-two fixed submanifolds*, Pacific J. Math.**173**(1996), no. 2, 387–401. MR**1394396****5.**F. Hirzebruch and D. Zagier,*The Atiyah-Singer theorem and elementary number theory*, Publish or Perish, Inc., Boston, Mass., 1974. Mathematics Lecture Series, No. 3. MR**0650832****6.**Katsuo Kawakubo,*The index and the generalized Todd genus of 𝑍_{𝑝}-actions*, Amer. J. Math.**97**(1975), 182–204. MR**0377949****7.**Robert D. Little,*Self-intersection of fixed manifolds and relations for the multisignature*, Math. Scand.**69**(1991), no. 2, 167–178 (1992). MR**1156424****8.**David C. Royster,*An analogue of the stabilization map for regular 𝑍_{𝑝} actions*, Rocky Mountain J. Math.**24**(1994), no. 2, 689–708. MR**1277354**, 10.1216/rmjm/1181072427**9.**C. T. C. Wall,*Surgery on compact manifolds*, Academic Press, London-New York, 1970. London Mathematical Society Monographs, No. 1. MR**0431216**

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Additional Information

**Robert D. Little**

Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822-2330

Email:
little@math.hawaii.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06369-9

Received by editor(s):
May 19, 2000

Published electronically:
July 31, 2001

Communicated by:
Ralph Cohen

Article copyright:
© Copyright 2001
American Mathematical Society