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Journal of the London Mathematical Society 1992 s2-45(2):352-362; doi:10.1112/jlms/s2-45.2.352
© 1992 by London Mathematical Society
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© Oxford University Press

A Duality Theorem for the De Rham Theory of a Family of Manifolds

M. A. Singer

Mathematical Institute Oxford 0X1 3L3

The family of manifolds Y/Z = (g1(z))z{varepsilon};z (where g: Y -> Z is a smooth map of maximal rank) is considered, and its de Rham theories H*(Y/Z) and H*(Y/Z) are defined from various points of view. It is proved that these theories are linked by a duality theorem (which reduces to Poincare duality when Z is reduced to a point). A localisation theorem which relates H*{Y/Z) to the homology groups H*(g–l(z)) is also given.


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