Geodesic
BOUNDS ON THE DIMENSION OF MANIFOLDS WITH INVOLUTION FIXING Fn ∪ F2
Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 595-604

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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.
DOI : 10.1017/S001708950800445X
Mots-clés : (2.000 Revision) Primary 57R85, Secondary 57R75 
PERGHER, PEDRO L. Q.; FIGUEIRA, FÁBIO G. BOUNDS ON THE DIMENSION OF MANIFOLDS WITH INVOLUTION FIXING Fn ∪ F2. Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 595-604. doi: 10.1017/S001708950800445X
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