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BOUNDS ON THE DIMENSION OF MANIFOLDS WITH INVOLUTION FIXING Fn ∪ F2

Published online by Cambridge University Press:  01 September 2008

PEDRO L. Q. PERGHER  and
FÁBIO G. FIGUEIRA
PEDRO L. Q. PERGHER
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos, SP 13565-905, Brazil e-mail: [email protected]
FÁBIO G. FIGUEIRA
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos, SP 13565-905, Brazil e-mail: [email protected]
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Abstract

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Let Mm be a closed smooth manifold with an involution having fixed point set of the form Fn ∪ F2, where Fn and F2 are submanifolds with dimensions n and 2, respectively, where n ≥ 4 is even (n < m). Suppose that the normal bundle of F2 in Mm, μ → F2, does not bound, and denote by β the stable cobordism class of μ → F2. In this paper, we determine the upper bound for m in terms of the pair (n, β) for many such pairs. The similar question for n odd (n ≥ 3) was completely solved in a previous paper of the authors. The existence of these upper bounds is guaranteed by the famous 5/2-theorem of Boardman, which establishes that, under the above hypotheses, m ≤ 5/2n.

Keywords

(2.000 Revision) Primary 57R85Secondary 57R75
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 595 - 604
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Boardman, J. M., On manifolds with involution, Bull. Amer. Math. Soc. 73 (1967), 136–138.Google Scholar
2.Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces, I, Amer. J. Math. 80 (1958), 458–538.Google Scholar
3.Conner, P. E. and Floyd, E. E., Differentiable periodic maps (Springer-Verlag, Berlin, 1964).Google Scholar
4.Suzanne, M.Kelton, Involutions fixing IRPj ⋃ F n, Topology Appl. 142 (2004), 197–203.Google Scholar
5.Suzanne, M.Kelton, Involutions fixing IRPj ⋃ F n, II, Topology Appl. 149 (1–3) (2005), 217–226.Google Scholar
6.Kosniowski, C. and Stong, R. E., Involutions and characteristic numbers, Topology 17 (1978), 309–330.Google Scholar
7.Pergher, P. L. Q. and Fabio, G. Figueira, Dimensions of fixed point sets of involutions, Arch. Math. (Basel) 87 (3) (2006), 280–288.CrossRefGoogle Scholar
8.Pergher, P. L. Q. and Fabio, G.Figueira, Involutions fixing F n ⋃ F 2, Topology Appl. 153 (14) (2006), 2499–2507.Google Scholar
9.Pergher, P. L. Q. and Fabio, G. Figueira, Two commuting involutions fixing F n ⋃ F n−1, Geom. Dedicata 117 (2006), 181–193.Google Scholar
10.Pergher, P. L. Q. and Stong, R. E., Involutions fixing {point} ⋃ F n, Transform. Groups 6 (2001), 78–85.Google Scholar
11.Royster, D. C., Involutions fixing the disjoint union of two projective spaces, Indiana Univ. Math. J. 29 (2) (1980), 267–276.Google Scholar