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Matveev S.V. — Lectures on Algebraic Topology
Matveev S.V. — Lectures on Algebraic Topology

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Название: Lectures on Algebraic Topology

Автор: Matveev S.V.


Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 98

Добавлена в каталог: 12.07.2008

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Предметный указатель
Abelianization      68
Atlas      18
Barycentric coordinates      85
Base space of a bundle      76
Boundary of a chain      8
Bundle      76
Bundle, locally trivial      77
Bundle, trivial      77
Category      1
Cell complex      43
Chain      7
Chain, complex      7
Chain, map      8
Change of charts      18
Chart      18
Complex, cell      43
Complex, chain      7
Complex, finitely generated      47
Complex, simplicial      6
Composition of morphisms      1
Connectedness      63
Contravariant functor      3
Covariant functor      2
Covering      79
Critical value      21
CYCLE      8
Deducibility      66
Defining relations      65
Diagrammatic search      9
Diffeomorphism      2
Dimension of a simplicial complex      7
Dual decomposition      58
Equivalent, bases      4
Equivalent, coverings      80
Equivalent, functors      38
Equivalent, words      65
Euler characteristic      48
Face of a simplex      5
Fibre of a bundle      76
Five-lemma      38
Free Abelian group      39
Functor, contravariant      3
Functor, covariant      2
Functor, forgetful      83
Fundamental group      63
Generators of a group      39 65
Group, cochain      53
Group, cohomology      54
Group, homology      11
Group, of coboundaries      53
Group, of cocycles      53
Homogenous polyhedron      58
Homologous cycles      8
Homology group      8
Homology, cellular      45
Homology, simplicial      11
Homology, singular      46
Homomorphism, functorial      36
Homomorphism, induced      64
Homotopic, loops      61
Homotopic, maps      15
Homotopy equivalence      2
Hurewicz homomorphism      76
Immersion      25
Immersion, standard      26
Incidence coefficient, of cells      44
Incidence coefficient, of simplices      10
Independent points      5
Induced orientation      6
Isomorphic, bundles      77
Isomorphic, objects      2
Knot complement      69
Kuenneth formula      57
Lebesgue number      16
Lefschetz number, homological      48
Lefschetz number, of a map      49
Lefschetz number, of endomorphism      47
Lefschetz Theorem      49
Length of a word      65
Lift, of a homotopy      77
Lift, of a map      77
Local coordinate system      18
Local homeomorphism      79
Loop      61
Manifold      18
Manifold, orientable      19
Manifold, piecewise-linear      19
Manifold, smooth      19
Maximal tree      71
Morphism of a category      1
Natural transformation      38
Object of a category      1
Orientation, induced      6
Orientation, of ${\mathbb{R}}^{N}$      4
Orientation, of a simplicial complex      7
Polyhedron      6 11
Polyhedron, acyclic      50
Polyhedron, topological      12
Projection of a bundle      76
Regular, covering      81
Regular, curve      25
Regular, homotopy      25
Regular, value      21
Relations in a group      39
Simple loop      26
simplex      5
Simplex, face of      5
Simplex, orientation of      5
Simplex, support plane of      5
Simplex, vertex of      5
Simplicial, complex      6
Simplicial, map      13
Singular, homology      46
Singular, point      21
Singular, simplex      46
Singular, triangulation      43
Skeleton of a cell complex      44
Spheroid      74
Star      15
Subdivision      14
Support plane      5
Tensor product, of chain complexes      55
Tensor product, of groups      51
Topological polyhedron      12
Torsion, product      52
Torsion, subgroup      47
Torus Knot      72
Total space of a bundle      76
Trace of an endomorphism      47
Triangulation      7
Underlying space of a simplicial complex      6
Universal coefficient theorem      51
van Kampen theorem      68
Vertex of a simplex      5
wedge      70
Wirtinger presentations      72
Writhe number      25
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