A structured visual guide to the major mathematical areas and their relationships.
Search by code, branch, topic, subtopic, or a keyword from the descriptions.
This subtopic introduces the core ideas in topological and transformation geometry, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Topological geometry studies incidence and geometric structures endowed with continuous topology, linking synthetic geometry with topological methods.
Topological geometry (Wikipedia)
Used to formulate geometric axioms compatible with continuity and deformation.
This topic investigates projective and affine incidence systems in which point and line sets carry natural topologies and continuity constraints.
Provides a framework for understanding geometric continuity in projective and affine settings.
Nonlinear incidence geometries such as Mobius and Laguerre type systems are studied here under topological regularity assumptions.
Useful for unifying incidence-theoretic and topological aspects of circle and sphere configurations.
This branch studies incidence and transformation structures realized on manifolds, often combining local geometric data with global topology.
Used when geometric structures are embedded in smooth or topological manifolds.
Differentiable incidence geometries combine synthetic concepts with smooth charts, tangent structures, and differentiable transformations.
Wikipedia: Differential geometry
Provides local analytic tools for otherwise synthetic geometric systems.
Here geometric incidence ideas interact with algebraic manifolds, often using algebraic and topological invariants simultaneously.
Useful for bridging synthetic geometry and algebraic geometry perspectives.