Manifolds (Mathematics) Algebraic topology Geometry, Differential Moduli theory Variétés (Mathématiques) Vector bundles Algebraic topology -- Research exposition (monographs, survey articles) Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants Compact analytic spaces Differentiable structures Differential geometry Differential geometry -- Global differential geometry -- Geometric evolution equations (mean curvature flow, Ricci flow, etc.) Differential geometry -- Global differential geometry -- Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) Differential geometry -- Symplectic geometry, contact geometry -- Floer homology and cohomology, symplectic aspects Differential geometry -- Symplectic geometry, contact geometry -- Geometric quantization Differential geometry -- Symplectic geometry, contact geometry -- Global theory of symplectic and contact manifolds Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Global differential geometry [See also 51H25, 58-XX; for related bund Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Research exposition (monographs, survey articles) Differential topology Floer homology Floer homology and cohomology, symplectic aspects Four-manifolds (Topology) Functions of a complex variable {For analysis on manifolds, see 58-XX} Functions of a complex variable {For analysis on manifolds, see 58-XX} -- Riemann surfaces Geometric evolution equations (mean curvature flow, Ricci flow, etc.) Geometric quantization Geometry Géométrie Géométrie différentielle