(Z₂)～k-actions With Fixed Point Set Of Constant Codimension 2～k+5

We discuss some properties of (Z₂)^k-actions with fixed point set of constant codi-mension 2^k + 5. Let φ : (Z₂)^k × Mⁿ → Mⁿ denote a smooth action of the group (Z₂)^k = {T₁,…,T_k|T_i² = 1,T_iT_j = T_jT_i} on a closed manifold Mⁿ. The fixed point set F of the action is the disjoint union of closed submanifolds of Mⁿ, which are finite in number. If each component of F is of constant dimension n — r, we say that F is of constant codimension r. If a n-dimensional unoriented cobordism class α_n contains a representative that admits a (Z₂)^k-action with fixed point set of constant codimension r, we denote that by α∈J_n,k^rk. J_*,k^r = ∑_n≥r J_n,k^r,is an ideal of the unoriented cobordism ring MO_* = ∑_n≥0 MO_n. In this paper, we determine J_*,k^2k+5 by constructing ingeniously indecomposable manifolds M which can be generators in MO_* and defining appropriate (Z₂)^k-action on M.