Manifolds of Preferences and Equilibria

Focusing on the mathematical study of preference spaces, this work employs differential topology and global analysis to explore local and global properties relevant to general equilibrium and utility analysis. It builds on Gerard Debreu's foundational approach, demonstrating that smooth preference spaces can be represented as differentiable Hilbert manifolds. The text extends key results regarding equilibrium regularity and examines topological properties of these manifolds, providing insights into agent utilities and demands while suggesting new research avenues in economics and mathematics.