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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: pergher@dm.ufscar.br
FÁBIO G. FIGUEIRA
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos, SP 13565-905, Brazil e-mail: fabio@dm.ufscar.br
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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

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