Revision #556 → #1245 · back to history
addedFundamental group (informal)21acbafa66c3
addedHomotopy invariance of fundamental groupf0f1f2c0e38c
addedLoop based at a point35fe995447fb
addedHomotopy of loopsa47bba6227c7
addedHomotopy is an equivalence relationbebf1f079531
addedFundamental group at a base point9d1085e65df7
addedProduct of loops (concatenation)a9435172903c
addedWell-defined product on homotopy classes6169dbb3e498
addedGroup structure on fundamental group78c9e994061f
addedAssociativity up to homotopya0f61ff7ef99
addedBase point independence for path-connected spaces5b1204f24d68
addedTrivial fundamental group of Euclidean / contractible spacesf2886a602a2a
addedSimply connected spacebf3c1d5160c6
addedSpheres are simply connected43e24c6e1ae6
addedFundamental group of the circleb0d2a39a6ad3
addedFundamental group of the figure eight29e01436ea81
addedFundamental group of a bouquet of circles200d08eb9e94
addedFundamental group of a wedge sum1207e77d8744
addedFundamental group of the punctured plane0710637dc614
addedFundamental group of a graph is freef3ee63da1182
addedGraph of 16 vertices in 4 rowsfa37b7f3e180
addedKnot groupbd323da54251
addedKnot group of the trefoild783b6faa195
addedFundamental group of an orientable surface868358dbd0fc
addedFundamental group of the torusc544dbc7fb03
addedFundamental group of a topological group is abelian63f3f666c9ec
addedEckmann–Hilton argument for H-spaces5bac8e42701a
addedFundamental group of an H-space is abelianf22f5a6631ac
addedInduced homomorphism319dceaa5f61
addedFundamental group is a functor84f0ecc9d225
addedHomotopy equivalent spaces have isomorphic fundamental groups25d037b9ba1a
addedFundamental group preserves products and coproducts89704c1c7c07
addedSeifert–van Kampen theorem9bc3bc5bb778
addedHurewicz theorem (first homology)e42b287f5797
addedFirst homology is the abelianization54e4a40e8e4d
addedFundamental group of a wedge as free productd6577fc79520
addedCovering spacec189a2651413
addedUniversal covering8be274b7f065
addedDeck transformations identify with fundamental group044a3945ee69
addedExistence of universal covering6a7c5bce66cc
addedUniformization theoremee0d2a996d56
addedFundamental group of a free quotient479d3769b0c0
addedFundamental group of real projective space22d339918e2a
addedFundamental group of homogeneous space G/H3dd35f3441c4
addedUniversal covering of a topological group is a topological group1695fafa1ae6
addedKernel of covering lies in centere77985b1b51c
addedUniversal covering groupcbb76ed7991e
addedLong exact sequence of a fibration024393cd599f
addedFibration reduces to isomorphism when base is simply connected72e2efb5ed71
addedFiber sequence for SU(n)6b3783c412b2
addedSU(n) is simply connected5d162b4c2781
addedNoncompact Lie groups reduce to compact case15833d8226fa
addedFundamental group via maximal torus and corootsbc2cb8513fa1
addedEdge-path and edge-equivalence826d00c94ce8
addedEdge-path group90e45419f68f
addedEdge-path group is the fundamental groupe392c5571369
addedEdge-path group via generators and relations77c0d373d1b6
addedEvery finitely presented group is a fundamental group of a finite simplicial complexce30c5e48019
addedUniversal cover as simplicial complex via edge-pathsfae2292cbfef
addedEvery group is the fundamental group of a 2-dimensional CW-complexfd36ab8b1e69
addedFinitely presented groups realized by 4-manifoldsd5004e475cf2
addedRestrictions on 3-manifold fundamental groups71e574610705
addedRealization in compact Hausdorff spaces and measurable cardinals566746097b9c
addedHigher homotopy groups6a25c0cd39e9
addedHurewicz theorem for n-spherecd204062c440
addedLoop space2f8d1caa0942
addedFundamental group as path components of loop spacefba6a6384107
addedFundamental groupoid39d8110304bf
addedGroupoid reproduces fundamental group6720a9ca0e72
addedvan Kampen for fundamental groupoids12321c8ae50a
addedLocal systems correspond to representations of fundamental group5493926b0fa5
addedÉtale fundamental groupe471482aa4a8
addedÉtale fundamental group as profinite completion3403b0818286
addedFundamental group of a root system / algebraic group244c5041ff16
addedFundamental group of a simplicial set810817540e91
addedHomotopy on 1-simplices of a Kan complexfa3dff088136