Viktor Majewski (Berlin) will give the geometry seminar at 2pm on 27th October, in the Salle des Profs (9th floor building NO). His title is “Spin(7)-Orbifold Resolutions” and his abstract is below.
By the seminal work of Joyce on the construction of compact exceptional holonomy metrics, it is known that exceptional holonomy orbifolds naturally arise on the boundary of the corresponding moduli spaces. In this talk, we discuss a general resolution scheme for exceptional holonomy orbifolds in the case of Spin(7)-metrics. We introduce smooth Gromov–Hausdorff resolutions as the appropriate notion of exceptional holonomy orbifold resolutions. We identify the necessary geometric data required to construct adiabatic torsion-free Spin(7) orbifold resolutions and prove that, under the vanishing of an obstruction arising from string cohomology, these adiabatic torsion-free Spin(7) resolutions can be deformed to genuine torsion-free Spin(7) metrics. This framework recovers Joyce’s generalized Kummer construction as well as the Joyce-Karigiannis construction of “mild” G2 orbifolds. Finally, we present new compact examples of Spin(7)-manifolds, including a family exhibiting a neck-stretching phenomenon.