论文标题
Galois覆盖物的相对L^2索引定理
The relative L^2 index theorem for Galois coverings
论文作者
论文摘要
考虑到完全自旋歧管的Galois覆盖物，基本度量在无穷大附近具有PSC，我们证明，对于足够小的epsilon> 0，dirac操作员的epsilon光谱投影在Atiyah von noumann代数中具有有限的痕迹。这使我们能够在偶数情况下定义L2索引，并证明其与Xie-Yu更高索引的兼容性。我们还推断出经典的Gromov-Lawson相对指数定理的L2版本。最后，我们简要讨论了一些Gromov-Lawson L2不变式。
Given a Galois covering of complete spin manifolds where the base metric has PSC near infinity, we prove that for small enough epsilon > 0, the epsilon spectral projection of the Dirac operator has finite trace in the Atiyah von Neumann algebra. This allows us to define the L2 index in the even case and we prove its compatibility with the Xie-Yu higher index. We also deduce L2 versions of the classical Gromov-Lawson relative index theorems. Finally, we briefly discuss some Gromov-Lawson L2 invariants.
