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Cobordisms of fold maps of 2k+2-manifolds into 3 k + 2

Tamás Terpai (2008)

Banach Center Publications

We calculate the group of cobordisms of k-codimensional maps into Euclidean space with no singularities more complicated than fold for a 2k+2-dimensional source manifold in both oriented and unoriented cases.

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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