G2-moduli spaces: geometry, periods and degenerate limits

Thesis

The overarching theme of the present dissertation is the geometry of compact 𝐺₂-manifolds and their moduli spaces. This thesis can be roughly divided into two parts: the first one is concerned with the spectral properties of twisted connected sums, whilst the second one studies the geometry of 𝐺₂-moduli spaces.

In the first part, we prove a deformation theorem allowing to construct torsion-free 𝐺₂-structures with 𝐶ᵏ-estimates (for any 𝑘 ≥ 1), and use it to deduce improved estimates ...

Expand abstract

Authors: Langlais, T

• DOI: 10.5287/ora-6rxrqzkrb
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: degenerate limits; G2-manifolds; holonomy; periods; moduli spaces
• Subjects: Geometric analysis; Geometry, Differential