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Z k -actions with a special fixed point set

Pedro L. Q. Pergher, Rogério de Oliveira (2005)

Fundamenta Mathematicae

Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if N m is any smooth and closed m-dimensional manifold with m > n and T : N m N m is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions ( M m ; Φ ) of the group G = Z k on closed smooth m-dimensional manifolds M m for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F. L. Capobianco,...

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