Manifolds with involutions whose fixed point set has constant codimension (Q752555)

Let \(J^ k_ n\) be the set of cobordism classes in the n-dimensional unoriented cobordism group \({\mathcal N}_ n\) which are represented by an n- dimensional manifold with smooth involution whose fixed point set is (n- k)-dimensional. Several authors have given necessary and sufficient conditions in terms of Stiefel-Whitney numbers for a class \(\alpha\in {\mathcal N}_ n\) to belong to \(J^ k_ n\). \textit{R. E. Stong} [Trans. Am. Math. Soc. 178, 431-447 (1973; Zbl 0267.57025)] has given such a condition for \(k=2\); \textit{F. L. Capobianco} [Proc. Am. Math. Soc. 61, 157-162 (1976; Zbl 0344.57013); Michigan Math. J. 24, 185-192 (1977; Zbl 0377.57007)] for \(k=3,4\); \textit{K. Iwata} [Proc. Am. Math. Soc. 83, 829-832 (1981; Zbl 0479.57022)] for \(k=5\); \textit{T. Wada} [Bull. Yamagata Univ., Nat. Sci. 10, 193-205 (1981)] for \(k=6\); and \textit{R. E. Stong} [Math. Z. 178, 443-447 (1981; Zbl 0469.57027)] for \(k=[(n-1)/2]\). The paper under review extends the results to \(k\leq 40\) if k is even and to \(k\leq 19\) if k is odd.