A Hausdorff, second-countable topological space locally homeomorphic to ℝ^n with C^∞-compatible charts. Setting for differential geometry, GR, gauge theory.
Smooth manifold
Related concepts
- Hausdorff (T₂) space
- Continuous map
- Differential geometry (manifold)
- Tangent space T_p M
- Riemannian metric
- Symplectic manifold
- Elliptic curve
- Riemann surface
- Lie group
- de Rham cohomology
- Poincaré duality
- Morse theory
- Symplectic manifold
- Contact manifold
- Principal G-bundle
- Symplectic form
- Morse theory: critical-point indices, handle-attachment, Morse inequalities
- Banach manifold: charts into Banach spaces + Fréchet-derivative calculus
- Jet bundle J^k(M,N): truncated Taylor fibre + prolongation functor
- Bianchi I (algebraic): R^ρ_{[σμν]}=0; II (differential): ∇_{[λ}R_{|σ|μν]}=0