A categorified excision principle for elliptic symbol families

Markus Upmeier* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We develop a categorical index calculus for elliptic symbol families. The categorified index problems we consider are a secondary version of the traditional problem of expressing the index class in K-theory in terms of differential-topological data. They include orientation problems for moduli spaces as well as similar problems for skew-adjoint and self-adjoint operators. The main result of this paper is an excision principle that allows the comparison of categorified index problems on different manifolds. Excision is a powerful technique for actually solving the orientation problem; applications will appear in companion papers Joyce–Tanaka–Upmeier [16], Joyce–Upmeier [17] and Cao–Gross–Joyce [8]
Original languageEnglish
Pages (from-to)1099–1132
Number of pages34
JournalQuarterly Journal of Mathematics
Issue number3
Early online date13 Jan 2021
Publication statusPublished - 1 Sep 2021


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