Revision #112 → #1149 · back to history
addedDefinition of diffeomorphism (intro)7d6c266e211e
addedDefinition of C^r-diffeomorphismbf7b7f7a0500
addedDefinition of diffeomorphic manifolds515f62dd5800
addedC^0-diffeomorphism is a homeomorphism050cc81a55c4
addedSmooth map between subsets of manifolds0f39b8568acc
addedDiffeomorphism of subsets of manifoldscf02ebd890c2
addedHadamard-Caccioppoli theoremb57072d44b46
addedComplex squaring map is not a diffeomorphism (simply connected needed)48c86ab82c42
addedDifferential is invertible iff it is a bijection (Jacobian criterion)1ba54825b42d
addedDiffeomorphisms preserve dimension6d5de2cde681
addedDefinition of local diffeomorphismb6976d590c0c
addedDefinition of submersione5952a18fdc1
addedDefinition of immersion39e095a6486f
addedx^3 is a homeomorphism but not a diffeomorphism9838c8de9469
addedEvery diffeomorphism is a homeomorphism (but not conversely)cb0cd850cf6a
addedExplicit map f with Jacobian zero on axesd71d37c250cf
addedLocal diffeomorphism criterion via linear independence of linear terms9e241f659b38
addedMap h with everywhere-zero Jacobian determinant (image is the unit circle)dc14f0dcbfe3
addedJacobian matrix of a surface deformationf94a89c8f9bd
addedSurface diffeomorphisms preserve angles (conformal property)b8f15d6728f3
addedDefinition of the diffeomorphism group0269b1fd876c
addedDiffeomorphism group is not locally compact (for positive-dimensional M)b290193a926f
addedWeak and strong topologies agree on compact manifolds7e903bfd892e
addedWeak topology is always metrizableedd3a0e381f2
addedStrong topology is Baire but not metrizable (noncompact case)7f59fa56363c
addedDiffeomorphism group is locally homeomorphic to space of vector fields1ec246d12717
addedDiffeomorphism group is a Banach manifold (finite r, compact M)14908bf321af
addedDiffeomorphism group is a Frechet Lie group (r = infinity, compact M)0db6b7362a4a
addedLie algebra of the diffeomorphism groupb24d85901ab0
addedNatural inclusion of a Lie group in its diffeomorphism groupe2ca8c44c09e
addedDiff(R^n) has two components; GL is a deformation retract79f3130fb808
addedDiffeomorphism group of a finite set is the symmetric groupdcd0db08f358
addedDiffeomorphism group acts transitively on connected manifold3b7aa82bc198
addedAction on configuration space is multiply transitive (dim >= 2)eec3fb3c29b0
addedHarmonic extension of circle diffeomorphism yields disc diffeomorphism (Rado-Kneser-Choquet)3a4f0e6c5295
addedOrientation-preserving diffeomorphism group of the circle is pathwise connected3acc11d5da4d
addedDiff(S^1) has the homotopy type of O(2)01a06730bedf
addedGroup of twisted spheres9225ab338875
addedMapping class group5757b5b0baff
addedSurface mapping class group is finitely presented, generated by Dehn twistscd27102ad4c3
addedMapping class group equals outer automorphism group of fundamental group (surfaces)d84f9e328f57
addedThurston classification: periodic, reducible, or pseudo-Anosovce2ca230c0b1
addedIdentity component of orientation-preserving diffeomorphism group is simple (Thurston)146ee2a443fe
addedDiff(S^2) has the homotopy type of O(3) (Smale)a73e0e30d847
addedDiff(T^2) has the homotopy type of GL(2,Z) x T^20f74a596d052
addedDiff(surface of genus >= 2) has contractible componentsafc247777056
addedDiff(S^n) does not have the homotopy type of a finite CW-complex (n >= 6)23850372f91c
addedDiffeomorphic implies homeomorphic (converse fails in general)fa17897f5549
addedIn dimensions 1, 2, 3 homeomorphic smooth manifolds are diffeomorphic8c14324bf895
addedMilnor's exotic 7-spherec9b3987c483d
added28 oriented diffeomorphism classes of manifolds homeomorphic to S^79b2cefb0e795
addedExotic R^4: uncountably many non-diffeomorphic smooth structures4729e82d6965