Strong invariants of even-dimensional topological insulators of independent Fermions are expressed in terms of an invertible operator on the Hilbert space over the boundary. It is given by the Cayley transform of the boundary restriction of the half-space resolvent. This dimensional reduction is routed in new representation for the $K$-theoretic exponential map. It allows to express the invariants via the reflection matrix at the Fermi energy, for the scattering set-up of a wire coupled to the half-space insulator.

中文翻译：

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偶数拓扑不变量的降维和散射公式

独立费米子的偶数维拓扑绝缘体的强不变量用边界上希尔伯特空间上的可逆算子表示。它由半空间解算器的边界限制的凯莱变换给出。这种降维以 $K$ 理论指数映射的新表示进行路由。它允许通过费米能量下的反射矩阵来表达不变量，用于耦合到半空间绝缘体的导线的散射设置。