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Gilles Englebert: Lectures

May 16, 2024
TITLE: Stability of Cayley fibrations

ABSTRACT: Motivated by the SYZ conjecture, it is expected that G_2 and Spin(7)-manifolds admit calibrated fibrations as well. One potential way to construct examples is via gluing of complex fibrations, as in the program of Kovalev. For this to succeed we need the fibration property to be stable under deformation of the ambient Spin(7)-structure, with the main difficulty being the analysis of the singular fibres. In this talk I will present a stability result for fibrations with conically singular Cayleys modeled on the complex cone {x^2 + y^2 + z^2 = 0} in C^3.

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