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Hajime Sato — Algebraic Topology: An Intuitive Approach
Hajime Sato — Algebraic Topology: An Intuitive Approach

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Название: Algebraic Topology: An Intuitive Approach

Автор: Hajime Sato


The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases.
In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references.
Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.

Язык: en

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 118

Добавлена в каталог: 20.11.2004

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Предметный указатель
(n-1)-dimensional sphere $S^{n-1}$      9
(unit) tangent sphere bundle      71
Atiyah-singer index theorem      100
Attaching map      12
Attaching space      12
Base point      17
Bidegree      83
Bigfaded abelian group      83
Bijection      106
Boundary axiom      30
Boundary of $\sigma^n$      44
Boundary operator      30 41
Bundle equivalent      72
Bundle homotopic      78
Bundle isomorphic      74
Bundle map      71
Bundle map, of vector bundles      74
Canonical vector bundle      76
Cell complex      13
Cell complex pair      16
Chain complex      41
Chain group      47
Characteristic class      79
Characteristic map      14
Chern class      96
Classifying space      78
Closed subset      108
Closed surface      13
Coboundary homomorphism      56
Coboundary operator      56
Cochain complex      57
Coefficient group      30
Cohomology theory      55
Collapsing spectral sequence      86
Composite      107
Connecting homomorphism      30
Continuous map      108
Convergent spectral sequence      83
Cup product      65
Derived couple      82
Diagonal map      64
Differential      30 84
Dimension axiom      30
Dimension of $\sigma^n$      44
Dimension of simplicial complex      45
Equivalence class      107
Euler number      99
Euler space      101
Euler — Poincare characteristic      99
Exact couple      81
Exact sequence      29
Exactness axiom      30
Excision axiom      30
Extension      63
Face      44
Fiber bundle      70
Fiber over a point      70
First homotopy group      20
First quadrant bigraded      83
Fundamental group      20
Generalized homology theory      31
Genus      13
Gysin cohomology sequence      98
Homeomorphic      2
Homotopic      3
Homotopy class      4
Homotopy invariance      31
Homotopy set      4
Homotopy type      4
Hopf map      71
Horneomorphism      2
Hornology      27
Hornology Stiefel- Whitney class      102
Identification topology      108
Incidence number      43
Index set      105
Induced (fiber) bundle      72
Injection      106
Integral homology      50
Isomorphic as vector bundles      74
Klein bottle      80
Link complex      100
Local triviality      73
Local trivialization      70
Mayer — Vietoris exact sequence      38
Mobius strip      11
n-dimensional ball $D^n$      9
n-simplex      44
Neighborhood      108
Orientation      47
p-boundary      47
p-cycle      41
Pointed topological space      17
Pontrjagin class      97
Product space      10
Pullback      72
q-coboundaries      57
q-cochain group      56
q-cocycles      57
q-skeleton      14
q-th homology group of simplicial complex      49
Quotient set      107
Quotient space      108
Quotient topology      108
Rank      100
Real projective plane      11
Real projective space      11
Reduced homology group      33
Regular cell complex      44
Relative topology      108
Restriction      107
Serre's spectral sequence      91
Set      105
Simplicial complex      45
Simplicial homology      50
Simply connected      20
Spectral sequence      83
Spectral sequence of fiber bundle      85
Splitting method      96
Stiefel — Whihtey class      97
Tensor product      61
Topological pair      5
Topological subspace      108
Topological sum      11
Torus      10
Total space      70
Triangulation      50
Trivial bundle      71
Universal coefficient theorem      66
Vector bundle      73
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