Abstract
We discuss several versions of the Family Signature Theorem: in rational cohomology using ideas of Meyer, in$KO[\tfrac {1}{2}]$-theory using ideas of Sullivan, and finally in symmetric$L$-theory using ideas of Ranicki. Employing recent developments in Grothendieck–Witt theory, we give a quite complete analysis of the resulting invariants. As an application we prove that the signature is multiplicative modulo 4 for fibrations of oriented Poincaré complexes, generalizing a result of Hambleton, Korzeniewski and Ranicki, and discuss the multiplicativity of the de Rham invariant.
Publisher
Cambridge University Press (CUP)
Cited by
1 articles.
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