(Z₂)^k-actions With Fixed Point Set Of Constant Codimension 2^k+9

letφ:(Z₂)^k×Mⁿ→Mⁿ denote a smooth action of the group (Z₂)^k={T₁,T₂,...,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. Let MO_n denote the unoriented cobordism group of dimension n and J_n,k^r the set of unoriented cobordism classes of Mⁿ that admits a (Z₂)^k-action with fixed point set of constant codimension r. J_n,k^ris a subgroup of MO_n and J_*,k^r=(?)_n≥r J_n,k^r an ideal of the unoriented cobordism ring MO_*=(?)_n≥0MO_n. In this paper, we determine J_n,k^2k+9 by constructing indecomposable manifolds M and defining a appropriate (Z₂)^k-action on M.