{"product_id":"9780691170459","title":"Annals Of Mathematics Studies","description":"\u003cdiv\u003e\n\u003cp\u003eAn 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.\u003c\/p\u003e \u003cp\u003eContent 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.\u003c\/p\u003e \u003cp\u003eReaders 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-dimensional spaces and the actions of groups on them.\u003c\/p\u003e \u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eKey content elements:\u003c\/strong\u003e cubical small-cancellation theory, Dehn filling in special cube complexes, structure and applications of right-angled Artin groups, hyperbolic groups formed as amalgams, and their topological consequences\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eLearning outcomes:\u003c\/strong\u003e solid understanding of cube complexes in geometric group theory, techniques for analyzing 3-manifolds, and the ability to apply cubical methods to complex problems\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eIllustration and writing style:\u003c\/strong\u003e rigorous proofs complemented by clear diagrams and geometric intuition, enhanced by more than 150 color figures\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eInteractive or standout features:\u003c\/strong\u003e structured developments that connect abstract theory to concrete topological questions, with attainable milestones for researchers advancing in the field\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eAudience:\u003c\/strong\u003e ideal for graduate students and researchers in geometry, algebra, and topology seeking a comprehensive, visually supported treatment\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eAfter finishing, readers gain a cohesive framework for approaching geometric group theory problems through cube complexes, a strengthened toolkit for exploring hyperbolic spaces and 3-manifolds, and renewed confidence to engage with advanced research questions. The work leaves a lasting impression of rigorous, interconnected ideas that expand both understanding and creative inquiry in modern geometry and topology.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"Crossword.in","offers":[{"title":"Default Title","offer_id":48540601614553,"sku":"9780691170459","price":6745.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0648\/3066\/9017\/files\/61cKJt-ZqYL._SL1500.jpg?v=1776677241","url":"https:\/\/www.crossword.in\/products\/9780691170459","provider":"Crossword.in ","version":"1.0","type":"link"}