An application of signature of smooth manifolds

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1994

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Virginia Tech

Abstract

We prove that no disjoint union of any number of copies of even dimensional complex projective space can bound a smooth oriented compact manifold with boundary. We prove this by defining and computing certain algebraic invariants for smooth oriented manifolds. A non-diffeomorphic relationship is established between boundary manifolds and complex projective space by contrasting invariants computed for these spaces.

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