Revision #527 → #1151 · back to history
addedChart on a topological spacec9ca6fd11ad4
addedDifferentiable atlasc1ee94b16da9
addedDifferentiably compatible chart43d82121be26
addedMaximal differentiable atlas962fd5480da0
addedSmooth structure / complex structure914ce0a5ad8f
addedEquivalent differentiable atlases1c7ba0a4ea5b
addedDimension well-defined on connected componentsf403c4b59055
addedDifferentiable manifold5e4e253ab9d2
addedC^0 manifold equals topological manifold63710f5338f9
addedPatching Euclidean pieces9fe0d0b9fb10
addedDifferentiable function on a manifold9d284fde6ab2
addedDirectional derivative along a curve1500fceb4cee
addedDirectional derivative depends only on tangent vectoraaf782d1d112
addedTangent vector and tangent spacece6a059afbcf
addedDifferential of a function at a point91b74ef8d437
addedTangent vector via local coordinates3a77d3f9cdf0
addedPartition of unity subordinate to a covere39b56657388
addedExistence of C^k partitions of unity50fad79931d4
addedC^k map between manifoldsa1d9ead48c5c
addedTangent bundle62ce43c6f287
addedCotangent space and cotangent bundle2b809d15fcc8
addedExact differentiala8db4423068d
addedTensor bundle53c437ffd483
addedFrame and frame bundlef7cb24cc0554
addedk-th order tangent bundle and jet bundles28cc286a9de5
addedk-th order frame bundle0854f51e19b8
addedDifferential / tangent map between manifoldsede83566eca9
addedImmersion, embedding and submersion7603ef0c14b7
addedImplicit function theorem for submersionsc211cee329e0
addedLie derivative1ebb2113fa9e
addedDifferential forms and degree61281e93d60b
addedExterior derivative2acffbbebc84
addedExterior derivative squared is zero0c0ff14da3f4
addedClosed and exact forms; de Rham cohomology6b64d9ae0b50
addedEquivalence of smooth atlases via diffeomorphismfbb07970bce0
addedSmooth structures in low dimensions0f066ffd9519
addedExistence of topological manifolds with no smooth structure873088b82a45
addedExotic 7-spheres (Milnor)b2396e62a856
addedClassification of 1-manifolds120c9047b3b9
addedClassification of compact 2-manifolds24be0ef92054
addedGeometrization conjecturec6440e1bc044
addedUndecidability of homeomorphism for 4-manifolds3252ea9abf0f
addedFreedman classification of simply connected 4-manifolds6ef18da3265d
addedBarden classification of simply connected 5-manifoldsd9913c4dd6f7
addedRiemannian manifolde4266b4a2aab
addedPseudo-Riemannian manifold87f8075d1fa6
addedFinsler manifold54a63bad267a
addedSymplectic manifold546b36b66b82
addedSymplectic manifolds are even-dimensional50bed18419ed
addedLie groupd9f05e16a38d
addedLie groups are parallelizable89d0a58744bd
addedPseudogroup0bb482d044b1
addedAtlas compatible with a pseudogroupd78f313c0e7e
addedManifolds as pseudogroup atlasescee1ad04d5d8
addedStructure sheaf giving a C^k manifold9c83dcabf0c5
addedDifferentiable manifold via locally ringed space6be4d2b1aecf
addedCotangent space via maximal ideald0b59b40a722
addedAlgebra of scalars on a manifoldd7b79b8fded8
addedReconstruction of M from algebra of scalars (Banach–Stone)e8b07fd391f2
addedPoints of M correspond to algebra homomorphismsef7516c42dae
addedTangent bundle via derivationse6aa75ab2da9