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| Lima E.L. — Fundamental Groups and Covering Spaces |
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| Предметный указатель |
Action of a group 154
Action, orbit of an 154
Action, transitive 154
Analytic continuation 124
Angle element 109
Base point 20 33
Change of variable formula 110
Circle eversion 104
Coherent atlas 186
Complex projective space 67
Complex projective space as a locally trivial fibration 69
Complex projective space, fundamental group of 71
Convenient neighborhood 130
Covering 125
Covering, automorphism 162
Covering, base of a 125
Covering, distinguished neighborhood 125
Covering, endomorphism 162
Covering, fiber of a 125
Covering, homomorphic 160
Covering, homomorphism 161
Covering, isomorphism 162
Covering, number of leaves of a 126
Covering, oriented double 192
Covering, product 193
Covering, regular 153
Covering, transformation 162
Covering, translation 162
Covering, universal 67 165
Curve, eversion of a 103 104
Curve, normal vector field to a 103 104
Curve, orientation of a 103
Curve, Peano 42
Curve, rotation number of a 99 103
Curve, simple 103
Curve, Space filling 42
Curve, winding number of a 95
Deformation retraction 22 23
Degree of a closed path 98
Degree of a map  58
Degree, local 111
Differential form 105
Differential form, closed 107
Differential form, exact 106
Differential of a function 106
Direction field 199
Distinguished neighborhood 63 68 125
Equivalence relation 28
Euler characteristic 180
Eversion, circle 104
Eversion, curve 103
Eversion, sphere 104
Fibration see locally trivial
Fibration fundamental group 25 33
Fibration fundamental group of a polyhedron 49
Fibration fundamental group of a surface 176
Fibration fundamental group of SO(n) 74 77
Fibration fundamental group of SU(n) 84
Fibration fundamental group of the circle 53 57
Fibration fundamental group of the complex projective space 71
Fibration fundamental group of the cylinder 58
Fibration fundamental group of the real projective space 66
Fibration fundamental group of the torus 57
Fibration fundamental group of U(n) 84
Fibration fundamental group, abelian 34 37 39 49
Fibration fundamental group, induced homomorphism 34
Fundamental grupoid 32
Graph 17
Graph, circuit of a 18
Graph, connected 18
Graph, edge of a 17
Graph, edge path 18
Graph, finite 18
Graph, free vertex of a 18
Graph, maximal tree of a 23
Graph, subgraph 18
Graph, tree 17
Graph, vertex of a 17
Group 28
Group of homeomorphisms 129
Group of spinors 173
Group, action of a 154
Group, conjugation of a 151
Group, isotropy 155
Group, monodromy 156
Group, properly discontinuous 130
Group, rotation 73
Group, simplectic 91
Group, special unitary 82
Group, topological 76
Group, unitary 82 84
Hermitian inner product 82
Homotopic maps 3
Homotopic paths 26
Homotopy 3
Homotopy of pairs 20
Homotopy, class 6 28
Homotopy, equivalence 10
Homotopy, free 28
Homotopy, inverse 10
Homotopy, linear 4
Homotopy, map extension and 13
Homotopy, one-parameter family and 6
Homotopy, path 25 26
Homotopy, regular 99 100
Homotopy, relative 26
Homotopy, relative to a subspace 20
Homotopy, type 10
Hopf fibration 78
Immersion 99
Isomorphic coverings 162
Isomorphism, orientation preserving 184
Isomorphism, positive 184
Isotopy 21
Klein bottle 169 192
Lifting 55 64 122
Local homeomorphism 119
Local homomorphism 143
Locally trivial fibration 68
Locally trivial fibration, complex projective space 69
Locally trivial fibration, distinguished neighborhood 68
Locally trivial fibration, global trivialization 69
Locally trivial fibration, hopf fibration 78
Locally trivial fibration, local trivialization 68
Locally trivial fibration, path lifting 70
Locally trivial fibration, product fibration 69
Locally trivial fibration, trivial fibration 69
Manifold, Banach 147
Manifold, coherent atlas 186
Manifold, compatible coordinate systems 186
Manifold, differentiable 185
Manifold, induced orientation 186
Manifold, maximal atlas 186
Manifold, opposite orientation of a 185
Manifold, orientable 185
Manifold, orientation of a 185
Manifold, oriented 185
Manifold, Riemannian 146
Map, analytic continuation of a 124
Map, closed 127 201
| Map, covering 125
Map, exponential 53
Map, extension 13
Map, inclusion 10
Map, k-th root of a 159
Map, lifting of a 122
Map, logarithm of a 158
Map, odd 61 72
Map, passing to the quotient 62
Map, proper 127 201
Map, quotient 119
Map, retraction 14
Map, section of a 123
Map, stereographic projection 41
Moebius band 188
normalizer 167
One-parameter family 3
Opposite points 65
Orbit of a point 130
Orientation of a manifold 185
Orientation of a plane curve 103
Orientation, induced 186
Orientation, product 188
Orthogonal couple 114
Pair of topological spaces 20
Parametrization, negative 31
Parametrization, positive 31
Parametrization, trivial 31
Path 25
Path lifting property 134
Path, angle function of a 55
Path, closed 26
Path, decomposition 32
Path, degree of a 53 55
Path, disorienting 197
Path, inverse of a 29
Path, lifting 64 70
Path, lifting of a 63
Path, lifting property 55
Path, operation with 28
Path, orienting 197
Path, parametrization 25
Path, partial 32
Path, piecewise  106
Path, product of 28
Path, rectilinear 145
Path, regular 99
Path, reparametrization 25
Path, winding number of a 96
Paths, nomotopic 26
Peano curve 42
Quaternion 75
Quaternion, conjugate of a 75
Quaternion, modulus of a 75
Quaternion, orthogonal 91
Quaternion, unit 75
Quotient space, fundamental property 62 68
Radial projection 7 8 10 96
Real projective space, fundamental group of 66
Real projective space, metric on the 64
Real projective space, orientation of 189
Regular curve 99
Regular homotopy 100
Regular path 99
Regular, homotopy 99
Reparametrization of a regular curve 99
retract 14
Retract, Euclidean neighborhood 15
Rotation number 99 103
Second homotopy group 92
Simplectic group 91
Simply connected space 40
SO(N) 73 74 77
Solid torus 57
Sp(N) 91
Space figure 8 99 103 114 139 153 154 170 179 180
Space filling curve 42
Space of type ENR 15
Space, contractible 11
Space, convex 12
Space, covering 125
Space, covering of a 125
Space, lens 170
Space, real projective 62 189
Space, semi-locally simply connected 142
Space, star 12 47
Special unitary group 82
Sphere eversion 104
Stabilizer 155
Stereographic projection 41
SU(N) 82 84
Subgroup, conjugate 151
Subgroup, normal 151
Theorem, Borsuk 16
Theorem, Borsuk — Ulam 61
Theorem, Brower fixed point 60
Theorem, Fundamental theorem of Algebra 98
Theorem, Gram — Schmidt orthonormalization 23 81 83
Theorem, Graustein — Whitney 98 101 104
Theorem, Hahn — Mazurkiewickz 42
Theorem, Hopf 103
Theorem, Koebe uniformization 178
Theorem, Mean Value Theorem 146
Theorem, Poincare 80
Theorem, Poincare — Bendixon 61
Theorem, Poincare — Bohl 4
Theorem, rank 77
Theorem, Rouche 96 98
Theorem, Sard's 43 86
Theorem, Seifert — Van Kampen 46
Theorem, Tietze — Urisohn 13
Theorem, Umlaufsatz 103
Topological group 48
Topological space, base point of a 33
Topological space, multiplication in a 47
Topological space, simply connected 40
Topology, compact-open 6
Topology, quotient 62 67
Topology, uniform convergence 6
Torus 10 28
TREE see graph
Typical fiber 68
U(n) 82
Unique path lifting property 55 135
Unitary group 82 84
Urysohn function 17
Vector field on spheres 8
Vector field, index of a 115
Vector field, singularity of a 115
Vector space, basis of a 183
Vector space, equally oriented bases 183
Vector space, negative basis of a 184
Vector space, negative isomorphism of a 184
Vector space, opposite orientation 184
Vector space, orientation of a 183
Vector space, oriented 184
Vector space, positive basis of a 184
Vector space, positive isomorphism of a 184
Vector space, transition matrix 183
Winding number 105
Zorn Lemma 2
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