论文标题
边界的Witt空间的签名
Signatures of Witt spaces with boundary
论文作者
论文摘要
令M为带边界的紧凑平稳分层的伪行，满足了Witt的假设。在本文中，我们介绍了de rham签名和M的杂物签名，并证明了它们的平等。接下来，在Albin和Gell-Redman的最新工作中，我们扩展了我们以前的工作中建立的Atiyah-Patodi-Singer指数理论，该理论是在MM对一般情况下具有分层深度1的假设，并在Witt Space上具有签名公式。 以平行的方式，我们还通过Galois Group Gamma覆盖M的Galois。采用von Neumann代数，我们引入了De Rham伽玛签名和Hodge Gamma-signature并证明它们的平等性，因此将其扩展到Witt Space，在平滑的情况下，Lueck和Schick证明了结果。最后，在平滑的情况下扩展了Vaillant的工作，我们为霍奇伽玛签名建立了一个公式。结果，我们推断出基本结果将M'边界的Cheeger-Gromov Rho不变与M和M'的签名差。 我们以结果的两个几何应用结束了论文。
Let M be a compact smoothly stratified pseudomanifold with boundary, satisfying the Witt assumption. In this paper we introduce the de Rham signature and the Hodge signature of M, and prove their equality. Next, building also on recent work of Albin and Gell-Redman, we extend the Atiyah-Patodi-Singer index theory established in our previous work under the hypothesis that M has stratification depth 1 to the general case, establishing in particular a signature formula on Witt spaces with boundary. In a parallel way we also pass to the case of a Galois covering M' of M with Galois group Gamma. Employing von Neumann algebras we introduce the de Rham Gamma-signature and the Hodge Gamma-signature and prove their equality, thus extending to Witt spaces a result proved by Lueck and Schick in the smooth case. Finally, extending work of Vaillant in the smooth case, we establish a formula for the Hodge Gamma-signature. As a consequence we deduce the fundamental result that equates the Cheeger-Gromov rho-invariant of the boundary of M' with the difference of the signatures of M and M'. We end the paper with two geometric applications of our results.
