Annals Of Mathematics Studies

An advanced mathematical monograph that applies cube complexes to geometric group theory and 3-manifold topology. It introduces new cubical methods, including cubical small-cancellation theory and a cubical Dehn-filling framework, and surveys right-angled Artin groups within a unified geometric view. Aimed at graduate students and researchers in geometry, algebra, and topology, the tone is rigorous yet exploratory, inviting careful study and fresh insight. Content is presented through formal theorems, constructions, and richly illustrated diagrams (with extensive color figures). It traces a path from foundational cubical concepts to sophisticated results, including a remarkable theorem about hyperbolic groups built as amalgams, and it highlights applications such as the virtual fibering of cusped hyperbolic 3-manifolds and residual finiteness for certain one-relator groups with torsion. The work culminates in outlining a cubical program to address Thurston’s conjectures, showcasing how cubical methods can resolve deep questions in topology. Readers experience a careful blend of rigorous proofs and geometric intuition, reinforced by concrete examples that demonstrate how cubical techniques illuminate long-standing problems. The text is designed for cumulative study, with precise definitions and logical progressions that reward close engagement, while diagrams help visualize high