Bordism of two commuting involutions

Author:
Pedro L. Q. Pergher

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2141-2149

MSC (1991):
Primary 57R85; Secondary 57R75

DOI:
https://doi.org/10.1090/S0002-9939-98-04356-1

MathSciNet review:
1451825

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we obtain conditions for a Whitney sum of three vector bundles over a closed manifold, , to be the fixed data of a -action; these conditions yield the fact that if is the fixed data of a -action, where is the trivial one dimensional bundle, then the same is true for . The results obtained, together with techniques previously developed, are used to obtain, up to bordism, all possible -actions fixing the disjoint union of an even projective space and a point.

**1.**A. Borel and F. Hirzebruch,*On characteristic classes and homogeneous spaces;I*, Am. J. Math.**80**(1958), 458-538. MR**21:1586****2.**C. Kosniowski and R. E. Stong,*Involutions and characteristic numbers*, Topology**17**(1978), 309-330. MR**82a:57036****3.**D. C. Royster,*Involutions fixing the disjoint union of two projective spaces*, Indiana Univ. Math. J.**29**(1980), 267-276. MR**81i:57034****4.**P. E. Conner and E. E. Floyd,*Differentiable Periodic Maps*, Springer-Verlag, Berlin, 1964. MR**31:750****5.**P. L. Q. Pergher,*An equivariant construction*, Proc. Amer. Math. Soc.**119**(1993), 319-320. MR**93k:57065****6.**P. L. Q. Pergher,*Manifolds with -actions*, Proc. Amer. Math. Soc.**106**(1989), 1091-1094. MR**89m:57039****7.**P. L. Q. Pergher,*The union of a connected manifold and a point as fixed set of commuting involutions*, Topology Appl.**69**(1996), 71-81. MR**96m:57055****8.**P. L. Q. Pergher,*-actions fixing a product of spheres and a point*, Canad. Math. Bull.**38**(1995), 366-372. MR**96j:57045****9.**R. E. Stong,*Bordism and involutions*, Ann. of Math.**90**(1969), 47-74. MR**39:3503****10.**R. E. Stong,*Equivariant bordism and -actions*, Duke Math. J.**37**(1970), 779-785. MR**42:6847****11.**R. E. Stong,*Involutions fixing projective spaces*, Michigan Math. J.**13**(1966), 445-447. MR**34:6795**

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Additional Information

**Pedro L. Q. Pergher**

Affiliation:
Universidade Federal de São Carlos, Departamento de Matemática, Rodovia Washington Luiz, km. 235, 13.565-905, São Carlos, S.P., Brazil

Email:
pergher@power.ufscar.br

DOI:
https://doi.org/10.1090/S0002-9939-98-04356-1

Keywords:
$(Z_{2})^{2}$-action,
fixed data,
bordism class,
projective space bundle,
Whitney number,
Smith homomorphism

Received by editor(s):
November 7, 1996

Received by editor(s) in revised form:
December 12, 1996

Additional Notes:
The present work was partially supported by CNPq

Communicated by:
Thomas Goodwillie

Article copyright:
© Copyright 1998
American Mathematical Society