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Connections on central extensions, lifting gerbes, and finite-dimensional obstruction vanishing
Indranil Biswas, Markus Upmeier
Given a central extension of Lie groups, we study the classification problem of lifting the structure group together with a given connection. For reductive structure groups we intr…
On spin structures and orientations for gauge-theoretic moduli spaces
Dominic Joyce, Markus Upmeier
Let be a compact manifold, a Lie group, a principal -bundle, and the infinite-dimensional moduli space of connections on modulo gauge. For…
A categorified excision principle for elliptic symbol families
Markus Upmeier
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 t…
Closed almost-Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler
Mehdi Lejmi, Markus Upmeier
We show that a closed almost Kähler 4-manifold of globally constant holomorphic sectional curvature with respect to the canonical Hermitian connection is automatically Kä…
Integrability theorems and conformally constant Chern scalar curvature metrics in almost Hermitian geometry
Mehdi Lejmi, Markus Upmeier
The various scalar curvatures on an almost Hermitian manifold are studied, in particular with respect to conformal variations. We show several integrability theorems, which state t…