https://sguzman.github.io/marginalia/categories/topology/Recent content in Topology on MarginaliaHugoen-usThu, 12 Feb 2026 00:00:00 +0000https://sguzman.github.io/marginalia/posts/homological-algebra/Thu, 12 Feb 2026 00:00:00 +0000https://sguzman.github.io/marginalia/posts/homological-algebra/Homological algebra grew out of 19th-century topology and became a central 20th-century language for modern mathematics. This essay traces the field from early homology invariants (Riemann, Betti, Poincaré) through Noether’s structural viewpoint, the Eilenberg–Mac Lane categorical turn, the Cartan–Eilenberg synthesis of derived functors, and the Grothendieck/Verdier revolution of abelian and derived categories. It closes with late-20th and 21st century developments including dg- and infinity-categories, derived algebraic geometry, and ongoing computational practice.https://sguzman.github.io/marginalia/posts/topology/Thu, 12 Feb 2026 00:00:00 +0000https://sguzman.github.io/marginalia/posts/topology/A comprehensive, historically grounded survey of topology: its 18th-century precursors (Euler and early structural problems), its formal birth in the late 19th century (Poincare and analysis situs), its 20th-century axiomatization and algebraic revolution (point-set topology, homology, homotopy), and its modern frontiers and applications (manifold theory, low-dimensional topology, and topological methods in data science, physics, and engineering). The piece emphasizes topology’s qualitative viewpoint - invariance under continuous deformation - and maps major subfields and conceptual bridges to geometry and analysis.