论文标题
家庭签名定理
The family signature theorem
论文作者
论文摘要
我们讨论了家庭签名定理的几个版本：在合理的共同体中，使用迈耶的思想，以$ ko [\ tfrac {1} {2} {2}] $ - 使用沙利文的思想，最后在对称$ l $ - 理论中使用ranicki的思想。采用Grothendieck的最新发展 - Witt理论，我们对由此产生的不变性进行了非常完整的分析。作为一种应用，我们证明签名是用于定向庞加莱复合物的纤维化的乘法模量4，这是Hambleton，Korzeniewski和Ranicki的概括，并讨论了De Rham不变性的多重性。
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, generalising a result of Hambleton, Korzeniewski and Ranicki, and discuss the multiplicativity of the de Rham invariant.
