Tag
Applications
5 resources tagged “Applications” across the knowledge library.
5 items
Guide6 Aug 2026Derived and Stable CategoriesThe derived category, localisation at quasi-isomorphisms, triangulated structure, derived functors in the modern sense, and the stable module category.4 min readRead MoreGuide6 Aug 2026Finiteness Conditions on GroupsCohomological dimension of groups, the Stallings-Swan theorem, finiteness conditions FP_n and F_n, duality groups, and the role of torsion.4 min readRead MoreGuide6 Aug 2026Homological Algebra and Algebraic TopologyThe topological origins of homological algebra, singular and cellular chains, the Eilenberg-Zilber and Kunneth theorems in topology, classifying spaces, and the dictionary between the two subjects.4 min readRead MoreGuide6 Aug 2026Modular Representation TheoryRepresentation theory in characteristic dividing the group order, failure of semisimplicity, relative projectivity, complexity and support varieties, and the Quillen stratification.4 min readRead MoreGuide6 Aug 2026Nilpotent Groups and HomologyThe lower central series, homological characterisation of nilpotent quotients, the Stallings and Stammbach theorems, and applications to group presentations.3 min readRead More