论文标题
一对dirac型操作员在非紧凑型歧管上的相对ETA不变
The relative eta invariant for a pair of Dirac-type operators on non-compact manifolds
论文作者
论文摘要
令$ \ Mathcal {a} _0 $和$ \ Mathcal {a} _1 $为两个自动辅助fredholm dirac-type操作员，这些操作员定义在两个非compact歧管上。如果它们在无穷大时重合，以使相对热算子是微量级别，则可以定义其相对ETA功能，如紧凑型情况。此功能在零点的常规值，我们称之为$ \ Mathcal {a} _0 $和$ \ Mathcal {a} _1 $的相对ETA不变性，是ETA不变到非compact情况的概括。我们研究其变化公式和胶合法。特别是，在某些条件下，我们表明，这种相对ETA不变与以前使用强callias型运算符的APS索引定义的相对ETA不变性相吻合。
Let $\mathcal{A}_0$ and $\mathcal{A}_1$ be two self-adjoint Fredholm Dirac-type operators defined on two non-compact manifolds. If they coincide at infinity so that the relative heat operator is trace-class, one can define their relative eta function as in the compact case. The regular value of this function at the zero point, which we call the relative eta invariant of $\mathcal{A}_0$ and $\mathcal{A}_1$, is a generalization of the eta invariant to non-compact situation. We study its variation formula and gluing law. In particular, under certain conditions, we show that this relative eta invariant coincides with the relative eta invariant that we previously defined using APS index of strongly Callias-type operators.
