A Categorified Excision Principle for Elliptic Symbol Families

Abstract We develop a categorical index calculus for elliptic symbol families. The categorified problems we consider are secondary version of the traditional problem expressing class in K-theory terms differential-topological data. They include orientation moduli spaces as well similar skew-adjoint and self-adjoint operators. main result this paper is an excision principle that allows comparison on different manifolds. Excision powerful technique actually solving problem; applications will appear companion papers Joyce–Tanaka–Upmeier [16], Joyce–Upmeier [17] Cao–Gross–Joyce [8].