3 papers
math.DG2026
Non-Existence of Smooth Full-Holonomy Cayley Fibrations
Jianfeng Lin, Viktor F. Majewski, Jacek Rzemieniecki
We prove that every Cayley fibration of a compact torsion-free Spin(7)-manifold with full holonomy must have singular fibers. This confirms a long-standing expectation in the study…
math.DG2025
Spin(7)-Orbifold Resolutions
Viktor F. Majewski
We develop an analytic and geometric framework for resolving compact Spin(7)-orbifolds by smooth torsion-free Spin(7)-manifolds. These orbifolds arise naturally as boundary points…
math.DG2025
Dirac Operators on Orbifold Resolutions: Uniform Elliptic Theory
Viktor F. Majewski
We study Dirac operators on resolutions of Riemannian orbifolds by developing a uniform elliptic theory. The key idea is to view orbifolds as conically fibred singular (CFS) spaces…