Some computations in equivariant cobordism in relation to Milnor manifolds

摘要

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 ∈_* : Z_* (G)→ N_* be the homomorphism which forgets the G-action. We use Milnor manifolds (degree 1 hypersurfaces in RP~m × RP~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(∈_*).