Some computations in equivariant cobordism in relation to Milnor manifolds

Let N ⁎ be the unoriented cobordism algebra, let G = ( Z 2 ) n and let Z ⁎ ( G ) denote the equivariant cobordism algebra of G-manifolds with finite stationary point sets. Let ϵ ⁎ : Z ⁎ ( G ) → N ⁎ be the homomorphism which forgets the G-action. We use Milnor manifolds (degree 1 hypersurfaces in R P m × R P n ) to construct non-trivial elements in Z ⁎ ( G ) . We prove that these elements give rise to indecomposable elements in Z ⁎ ( G ) in degrees up to 2 n − 5 . Moreover, in most cases these elements can be arranged to be in Ker ( ϵ ⁎ ) .