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Commuting involutions whose fixed point set consists of two special components

Pedro L. Q. Pergher, Rogério de Oliveira (2008)

Fundamenta Mathematicae

Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property when it has the following property: if N m is any smooth 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. Examples of manifolds with this property are: the real, complex and quaternionic even-dimensional projective spaces R P 2 n , C P 2 n and H P 2 n , and the connected sum of R P 2 n and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere and n is not...

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