Oriented and weakly complex bordism algebra of free periodic maps

Abstract

Free cyclic actions on a closed oriented (weakly almost complex, respectively) manifold which preserve the orientation (weakly complex structure) are considered from the viewpoint of equivariant bordism theory. The author gives an explicit presentation of the oriented bordism module structure and multiplicative structure of all orientation preserving (and reversing) free involutions. The odd period and weakly complex cases are also determined with the aid of the notion of formal group laws. These results are applied to a nonexistence problem for certain equivariant maps.

On Wall Manifolds with (ε)-Free Involutions

“…In §2, we state the image of each F B in Theorem 2 8 8 0 In §3, we study Wall manifolds with (e)-free involutions derived from some generators of @*(Zz)> the oriented bordism module of all orientation-preserving (or orientation-reversing) free involutions ( [5] Proof. For the proof of (i) , see the remark 2.…”