The Asymptotic Geometry of $\mathrm {G}_2$-Monopoles

Daniel Fadel, Universidade Federal do Rio de Janeiro, Brasil. Akos Nagy, University of California, Santa Barbara, CA. Goncalo Oliveira, Instituto Superior Tecnico, Lisboa, Portugal, and Institute of Science and Technology Austria, Klosterneuberg, Austria.

Chapters 1. Introduction 2. Preliminaries 3. Consequences of Moser iteration and $\varepsilon $-regularity 4. Finite mass from finite intermediate energy 5. Bochner-Weitzenbock formulas along the end 6. Refined asymptotics in the AC case 7. Boundary data 8. Bogomolny trick for the intermediate energy 9. Decay of linearized solutions 10. Weighted split Sobolev spaces: Fredholm operators 11. Weighted split Sobolev spaces: Sobolev Embeddings and Multiplication Maps 12. Moduli theory