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Tamura I. — Topology of lie groups, I and II
Tamura I. — Topology of lie groups, I and II

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Название: Topology of lie groups, I and II

Автор: Tamura I.

Аннотация:

Topology of Foliations was first published in Japanese in 1976, with the principal aim of introducing the theory of foliations to young students. The author, Professor Itiro Tamura, passed away on February 21, 1991, during the preparation of the English translation of this successful book.
Professor Tamura worked on differential topology in the late 1950's. His results included establishing the non-homotopy-invariance of the Pontrjagin classes, demonstrating the existence of a topological eight-manifold with no differential structure, etc. He began working on the theory of foliations in the late 1960's and made an important contribution to the problem of the existence of foliations on closed manifolds in 1971: he constructed codimension-one foliations on every odd-dimensional homotopy sphere. This was done by showing the existence of spinnable structures on such manifolds. This work stimulated the study of foliations, which grew very rapidly in the 1970's.
At almost the same time as the publication of the original version of this book, the problem of the existence of foliations on closed manifolds was solved by W. Thurston. Much work in foliation theory has been done since 1976. An important part of this work was done by Tamura's students, who had read the original version of Topology of Foliations, as the author had hoped.
The author himself was active in the theory of foliations. He initiated the theory of transverse foliations. In the last several years of his life, he was studying the Seifert conjecture and the minimal flow conjecture. I regret very much that he could not continue his research.
The Topology of Foliations was translated into Russian in 1979. Now an English translation has been completed and many more students of mathematics can touch the spirit of Itiro Tamura.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 197

Добавлена в каталог: 30.10.2010

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Предметный указатель
$C^{0}$ immersion      47
$C^{r}$ coordinate neighborhood system      40
$C^{r}$ curve      5
$C^{r}$ diffeomorphism      44
$C^{r}$ embedding      47
$C^{r}$ function      43
$C^{r}$ immersion      46
$C^{r}$ manifold      41 63
$C^{r}$ map      44
$C^{r}$ vector field      4 60
$m$-plane field      149
$m$-plane field, involutive      152
$m$-plane field, transverse to the boundary      165
$n$-ball      38
$n$-sphere      38
$q$-form      137 142
$q$-form over an open cover      149
$q$-form, $C^{r}$      142
$q$-form, differential      142
$x$-component      3
$y$-component      3
$\alpha$-limit set      68
$\omega$-limit set      68
$\varepsilon$-neighborhood      8 36
Accumulation point      3 8
Admissible point      103
Alternating form      139
Arcwise connected component      38
Arcwise connected set      38
Atlas      43 62
Atlas, foliated      82
Base space B      90
Basis for a topology      35
Boundary $\partial$M      63
Boundary of a set      37
Boundary point      63
Boundary points      37
Bracket product      152
Broken line      61
Bundle foliation      90
Chain      94
Characteristic class Godbillon — Vey      167
Chart      43 63
Chart, distinguished      93
Chart, foliated      82
Class $C^{r}$      10 19
Closed curve      11
Closed integral curve      68
Closed manifold      63
Closed set      3 8 35
Closed trajectory      13 68
Closure      3 8
Closure of a set      37
Cluster point      3 8
Cobordism class      162
Cobordism class, foliated      161
Cobordism foliated      161
Cobordism group      162
Cobordism group, foliated      161
Codimension      82
Coherent      102
Coherent chain      102
Coherent chain over a curve      103
Coherent chart-system      101
Cohomology class de Rham      167
Compact space      37
Compatible      42
Complete integrability      150 165
Connected component      36
Connected space      35
continuous curve      10
Continuous map      10 38
Convergent sequence      37
Coordinate neighborhood      41 63
Coordinate system      90
Countable basis      35
Covering space      91
Curve      51
Cycle vanishing      123
de Rham cohomology classes      167
De Rham cohomology group      167
Dense set      8
Dense subset      37
Diffeomorphism      19 44 63
Diffeomorphism, foliation-preserving      159
Diffeomorphism, local      113
Differentiable manifold      41
Differentiable map of class $C^{r}$      40
Differentiable of class $C^{r}$      4
Differential $g*dg$      59
Differential structure      43
Discrete space      36
Distinguished chart      93
Dual basis      137
Dual plane field      149
Dual space      137
Dynamical system      13 65
Embedding      63
Equivalence class      7
Ergodic point      20
Ergodic trajectory      13
Exterior algebra      139
Exterior derivative      143
Exterior product      139 143
Fiber bundle, $C^{r}$      89
Fiber bundle, locally constant      90
Fiber space, locally trivial      90
Fiber, F      90
Finite intersection property      37
Fixed vector      3
Foliated cobordism      161
Foliated cobordism class      161
Foliated cobordism group      161
Foliation      81
Foliation, $C^{r}$      81
Foliation, Reeb      85
Foliation, simple      90
Foliation, transverse to boundary      89 159
Foliation, transversely orientable      87
Form, alternating      139
Form, closed      145
Form, exact      145
Form, Godbillon — Vey      165
Form, linear      137
Germ      114
Godbillon — Vey characteristic class      167
Godbillon — Vey form      165
Godbillon — Vey number      168
Hausdorff space      36
Holonomy      115
Holonomy group      115
Homeomorphism      38
Homotopy of chains      105
Hopf map      71
Immersion      63
Induced orientation      64
Initial point      65
Integral curve      5 6 11 65
Integral curve starting at $-$      12 65
Integral curve through $-$      12 65
Integral of $q$-form      146
Integral of $\omega$      146
Interior      3 8
Interior of a set      37
Interior point      3 8
Invariant set      13 68
Jacobian matrix      45
Leaf      82
Leaf topology      86
Leaf topology, relative      86
Leaf, compact      86
Leaf, exceptional      86
Leaf, locally dense      86
Leaf, one-sided      110
Leaf, proper      86
Leaf, two-sided      110
Length      61
Length of a curve      61
Length of a homotopy      105
Length of chain      94
Lift      184
Limit point      3 8 37
Limit set      68
Local coordinate system      9
Local diffeomorphism      113
Locally finite cover      50
M$\ddot{o}$bius strip      91
Manifold      40
Manifold with boundary      63
Manifold without boundary      63
MAP      63
Metric      3 36
Metric axioms      3 36
Metric space      36
Metric topology      37
Minimal set      68
Mutually transversal foliations $\mathcal{F}$, $\mathcal{F}’$      89
Neighborhood      3 35
Neighborhood, foliated      82
Nonsingular vector field      4 10 60
One-form      137
Open cover      37
Open set      3 8 35
Open with respect to the metric $\rho$      36
Orbit      13 68
Orientable manifold      57
Orientation      58
Orientation-preserving      59
Orientation-preserving map      19
Orthogonality      60
Partition of unity      50
Periodic integral curve      13 68
Periodic point      20
Periodic trajectory      13 68
Plane field      149
Plane field, differentiable      149
Plaque $Q_{\lambda}$      93
Plaque chain      94
Poincar$\acute{e}$ — Bendixson Theorem      69
Point, admissible      103
Product bundle      90
Product manifold      43
Product space      36
Projection      56
Projection map      90
Rank of a map      45
Reeb foliation      85
Reflection      171
Relative topology      35
Representative (of equivalence class)      7
Riemannian metric      60
Seifert conjecture      72
Simple closed curve      47
Simple curve      11
Singular point      60
Singular point, zero      60
Solution curves      5 65
Sphere bundle      90
Submanifold      47 63
Submersion      49
subspace      35
Support      145
Support of a function      50
System of charts coherent      101
System of open sets      35
Tangent bundle      90
Tangent plane      9
Tangent plane field      149
Tangent plane field defined by one-forms      149
Tangent space $T(M)$      56
Tangent space $T_{p}(M)$      53
Tangent vector      5 11 53 65
Tensor product      138
Topological manifold      62
Topological space      35
Topological space with a countable basis      35
topology      35
Torus      7
Total space, E      90
Trajectory      5 13 68
Transversality $C^{r}$ vector field      60
Transverse curve      28
Transverse immersions      59
Transverse intersection      59
Two-sidedness of a coherent chart system      110
Unit tangent vector $e_{t}$      54
Vanishing cycle      123
Vector based at $-$      3
Vector field      4 10 60
Vector field, transverse to $\mathcal{F}$      87
Vector, parallel      172
Wedge product      139 143
Zero vector      3 9
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