(Z₂)～k-actions And Minimal Data Of Normal Bundle

Let denote the ideal in the unoriented cobordism ring MO* of classes containing a representative that admits a (Z2)k-action with fixed point set of constant dimension n - r.Suppose (Z2)k acts on the closed manifold Mn with fixed point set Fn-r so that then normal bundle of Fn-r in Mn decomposes as F and ordered set of the 2k - 1 vector bundles (i = 1,2,..., 2k- 1) constitute the fixed data of the action on Mn. Let I = non-negative integer} , that is the total non-negative integer solutions to the Diophantine equation I is said to be the set of total 2k - 1 partitions of r . Every element of I is said to be a 2k - 1 partition of r .For each subset denotes the set consisting of the classes a which is represented by the manifold Mn with (Z2)k-action having fixed data such that for each component F' of Let ||A|| represent the number of the elements of A . The Minimal data of normal bundle for Jr*,k is defined byIn this work , ||Jr*,k|| = 3 are obtained for r = 2, k > 2 and r = 3, k = 2 . Meanwhile , the smaller upper bound of ||Jr*,k|| are determined for r = 4, 5,6,k = 2 and r = 4, 6, k > 3. | reflects the complexity of the (Z2)k action on Mn.