(Z₂)^k-actions With Fixed Point Set Of Constant Codimension 2^k+13

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 n-dimensional 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 n dimensional unoriented cobordism classesα_n containing a representative Mⁿ admiting a (Z₂)^k-action with fixed point set of constant codimension r.J_*,k^r=∑_n≥rJ_n,k^T is an ideal of the unoriented cobordism ring MO_* =∑_n≥0MO_n.In this paper, we determine J_*,k^2k+13 by constructing indecomposable manifolds M and defining appropriate (Z₂)^k-action on M.