Involutions fixing the disjoint union of 3-real projective space with Dold manifold. (English) Zbl 0964.57032
This paper determines the cobordism classification of smooth involutions \((M,T)\) having fixed point set the union of the projective space \(\mathbb{R} P^3\) and a Dold manifold \(P(m,n)\). It is assumed that the normal bundle of \(\mathbb{R} P^3\) in \(M\) does not bound and that \(m\) and \(n\) are positive, so that the fixed set is genuinely such a union. The main results are that one must have \(m=3\) and \(n\) even. For each of the possible choices of the normal bundle of \(\mathbb{R} P^3\) there is exactly one possible stable normal bundle for \(P(3,n)\), and the range of dimensions for \(M\) is determined.
Reviewer: R.E.Stong (Charlottesville)
MSC:
| 57R85 | Equivariant cobordism |
| 57R90 | Other types of cobordism |
| 55N22 | Bordism and cobordism theories and formal group laws in algebraic topology |
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