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Vick J.W. — Homology theory. An introduction to algebraic topology
Vick J.W. — Homology theory. An introduction to algebraic topology

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Название: Homology theory. An introduction to algebraic topology

Автор: Vick J.W.

Аннотация:

This book is designed to be an introduction to some of the basic ideas in the field of algebraic topology. In particular, it is devoted to the foundations and applications of homology theory. The only prerequisite for the student is a basic knowledge of abelian groups and point set topology. The essentials of singular homology are given in the first chapter, along with some of the most important applications. In this way the student can quickly see the importance of the material. The successive topics include attaching spaces, finite CW complexes, the Eilenberg-Steenrod axioms, cohomology products, manifolds, Poincaré duality, and fixed point theory. Throughout the book the approach is as illustrative as possible, with numerous examples and diagrams. Extremes of generality are sacrificed when they are likely to obscure the essential concepts involved. The book is intended to be easily read by students as a textbook for a course or as a source for individual study. The second edition has been substantially revised. It includes a new chapter on covering spaces in addition to illuminating new exercises.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1994

Количество страниц: 242

Добавлена в каталог: 10.02.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acyclic model theorem      125
Adams, J.F.      30 140 227
Adem, J.      140 227
Alexander — Whitney diagonal approximation      133
Algebraic mapping cylinder      167
Antipodal map      28
Back j -face      133
Barycenter      211
Barycenter of affine singular simplex      214
Barycentric subdivision      212
Base space      85
Betti number      63
Bilinear form      176—182
Bilinear form, antisymmetric      176
Bilinear form, nonsingular      176
Bilinear form, signature of      179
Bilinear form, symmetric      176
Bilinear mapping      65
Bing, R.H.      218
Birkhoff, G.D.      209 227
Boundary      5
Boundary operator      4
Brouwer, L.E.J.      25 34 186
Brouwer, L.E.J., fixed-point theorem      25
Brown, M.      169 218 227
Brown, Robert E      209 210 227
Brown, Ronald      64 227
Brumfiel, G.      185 227
Cap product      140
Category      124
Cellular approximation theorem      96
Cellular map      60
Chain complex      5
Chain complex, homology      6
Chain complex, quotient of      44
Chain complex, subcomplex of      44
Chain homotopy      12
Cobordism      184
Cobordism, oriented      184
Cobordism, unoriented      185
Coboundary operator      77
Cochain complex      77
Cochain complex, homotopy      77
Cochain complex, map      77
Cocycle      78
Coefficient group      75
Cohomology group      78
Cohomology group, de Rham      207
Cohomology group, singular      78
Coincidence      188
Coincidence, class      195
Coincidence, index      189
Coincidence, number      188
Coincidence, theorem      198
Collaring theorem      169
Commutative graded R-algebra      132
Cone      214
Conelly, R.      218 223 227
Connecting homomorphism      19
Convex      1
Convex hull      1
Coordinate neighborhood      149
Covering map      85
Covering projection      85
Covering space      85
Covering space, automorphism of      103
Covering space, isomorphism of      102
Covering space, map of      102
Cross section      99
Cup product      132
Curvature      207
CYCLE      5
de Rham      183
de Rham, theorem      207
Deformation retract      17
Deformation retract, strong      49
Degree, local, at fixed point      194
Degree, of a loop      95
Degree, of antipodal map      28
Degree, of chain map      5
Degree, of map of manifolds      186
Degree, of map of spheres      25
Derivation property      129
Diagonal      36
Diagonal approximation      133
Diameter      211
Direct limit      30
Direct product      8
Direct sum      8
Direct system      30
Directed set      30
Disk      24
Dold, A.      189 218 227
Double of M      169
Dual cell      143
Eckmann, B.      29 227
Eilenberg — Steenrod axioms      74
Eilenberg — Steenrod axioms, uniqueness theorem      75
Eilenberg — Zilber theorem      128
Eilenberg, S.      74 140 167 227
Epstein, D.B.A.      84 228
Equivalence relation      8 35
Equivalence relation, generated      37
Equivalence relation, graph of      36
Euclidean half-space      146
Euler characteristic      63 188
Euler class      188
Exact sequence      17
Exact sequence, long      19
Exact sequence, short      17
Exact sequence, split      48
Excision theorem      46
exp (exponential map)      86
Ext      79
External product, cohomology      130
External product, homology      128
Face      3
Fadell, E.      209 227
Finite CW complex      54
Finite CW complex, subcomplex      56
Five lemma      46
Fixed-point index      191
Fixed-point theorem      199
Flow      207
Flow, fixed point of      208
Free Abelian group      3
Free product      115
Free product, amalgamated      115
Free resolution      70
Front i-face      133
functor      124
Functor, contravariant      124
Functor, covariant      124
Functor, free, with respect to models      125
Functor, natural transformation of      124
Fundamental class      156
Fundamental class of manifold with boundary      169
Fundamental group      92
Fundamental neighborhood      85
Fundamental theorem of algebra      204
Fundamental theorem of calculus      80
Gauss — Bonnet theorem      207
Generalized homology theory      77
Graded abelian group      5
Graded abelian group of finite type      141
Gray, B.      115 227
Hodge, W.V.D.      183
Homology group      6 (see also “Singular homology group”)
Homology theory      74
Homology theory, generalized      77
Homomorphism of covering spaces      102
Homotopy      13
Homotopy, equivalence      16
Homotopy, inverse      16
Homotopy, of map of pairs      45
Homotopy, type      16
Hopf invariant      135—140
Hopf invariant, for Hopf maps      176
Hopf map      42
Hopf, H.      25
Horizontal circle      86
Horn      77
Hu, S.-T.      140 227
Hurewicz homomorphism      107
Hurwitz and Radon      29
Index of fixed point      186
Index of manifold      179
Index of vector field      206
Integral coefficients      71
Interior      19
Invariance of domain      34
Isotopy      152
Jordan — Brouwer separation theorem      33
Kirby, R.      185 227
Knot      118
Knot, group of      119
Knot, torus      119
Knot, unknotted      119
Kronecker index      81
Kunneth formula for chain complexes      123
Kunneth formula for singular cohomology      141
Kunneth formula for singular homology      128
Lebesgue number      90
Lefschetz, S.      44 186 227
Lefschetz, S., class      195
Lefschetz, S., coincidence theorem      198
Lefschetz, S., fixed-point theorem      187 199
Lefschetz, S., number      187 195
Lifting problem      87
Lifting theorem      97
Locally pathwise connected      85
Long Exact Sequence      19
Madsen, I.      185 227
Manifold      146
Maps of pairs      45
Massey, W.S.      105 106 115 227 228
Mayer — Vietoris sequence      22
mesh      211
Milgram, R.J.      185 227
Milnor, J.W.      84 158 206 218 228
Mobius band      89
Models      125
Morphism      124
Mosher, R.E.      84 228
Multiplicity      106
Orientation      156
Orientation, double covering      156
Orientation, of manifold with boundary      169
Pair of spaces      45
Path components      9
Pathwise connected      7
Poincare group      92
Poincare — Hopf theorem      206
Poincare — Lefschetz duality theorem      171
Poincare, H.      186 209
Poincare, H., duality theorem      143 165—168
Poincare, H., last geometric theorem of      208
Poincare, H., relative form      171
Projective space, complex      41
Projective space, quaternionic      42
Projective space, real      37 40
Proper n-ball      155
Pushout      114
Quotient function      35
Rank of finitely generated abelian group      63
Rational homology sphere      201
Regular covering space      105
Relative homeomorphism      51
Relative homology group      45
Retraction      16
Right exact functor      69
Samelson, H.      143 189 228
Segment      1
Semilocally simply connected      105
Short exact      17
Siebenmann, L.      185 227
simplex      1
Simplex, ordered      2
Simplex, singular      2
Simplex, standard      2
Simply connected      91
Singer, I.M.      207 228
Singular chain      4
Singular chain of (X, A)      45
Singular cohomology group      78
Singular cohomology group, of sphere      83
Singular cohomology group, reduced      81
Singular cohomology ring of complex projective space      175
Singular cohomology ring of quaternionic projective space      176
Singular cohomology ring of real projective space      175
Singular cohomology ring of torus      135
Singular homology group      78
Singular homology group, additive property of      9
Singular homology group, of complex projective space      43
Singular homology group, of generalized torus      43
Singular homology group, of point      7
Singular homology group, of quaternionic projective space      43
Singular homology group, of real projective space      63
Singular homology group, of sphere      24
Singular homology group, reduced      48
Singular homology group, relative      45
Singular homology group, topological invariance      10
Singular homology group, with coefficients in G      71
Singular simplex      2
Singular simplex, affine      213
Skeletal chain complex      58
Skeleton      54
Spanier, E.H.      105 115 228
Sphere      23
Spherical class      43
Split exact      48
Star of vertex      143
Steenrod, N.E.      74 84 140 167 227 228
Stong, R.      185 228
Suspension      27
Tangora, M.C.      84 228
Tensor product      66
Tensor product of chain complexes      120
Thorn class      161
Thorn isomorphism theorem      160—162
Thorn isomorphism theorem for circle      162
Thorpe, J.A.      207 228
Topological cobordism ring      185
Topological manifold      146
Tor      70
Torus      41
Total space      85
Universal coefficient theorem      73
Universal covering space      105
Universal mapping property      105
van Kampen theorem      115
Vector field      29
Vertex      2
Vertical circle      87
Volume element      207
wedge      40
Whitehead, J.H.C.      136
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