دانلود کتاب Graphs, surfaces and homology

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Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface to the third edition......Page 13
Preface to the first edition......Page 15
Notation......Page 19
Introduction......Page 23
Abstract graphs and realizations......Page 31
Kirchhoff’s laws......Page 36
Maximal trees and the cyclomatic number......Page 38
Chains and cycles on an oriented graph......Page 42
Planar graphs......Page 48
Appendix on Kirchhoff’s equations......Page 57
2 Closed surfaces......Page 60
Closed surfaces and orientability......Page 61
Polygonal representation of a closed surface......Page 67
A note on realizations......Page 69
2.7. The reduction algorithm......Page 71
Euler characteristics......Page 77
Minimal triangulations......Page 82
Simplexes......Page 89
Ordered simplexes and oriented simplexes......Page 95
Simplicial complexes......Page 96
Abstract simplicial complexes and realizations......Page 99
Triangulations and diagrams of simplicial complexes......Page 101
Stars, joins and links......Page 106
Collapsing......Page 110
Appendix on orientation......Page 115
Chain groups and boundary homomorphisms......Page 121
Homology groups......Page 126
Relative homology groups......Page 134
Three homomorphisms......Page 143
Appendix on chain complexes......Page 146
5 The question of invariance......Page 149
Invariance under stellar subdivision......Page 150
Triangulations, simplicial approximation and topological invariance......Page 155
Appendix on barycentric subdivision......Page 158
The homology sequence of a pair......Page 160
The excision theorem......Page 164
Collapsing revisited......Page 166
Homology groups of closed surfaces......Page 171
The Euler characteristic......Page 176
The Mayer–Vietoris sequence......Page 180
Homology sequence of a triple......Page 189
8 Homology modulo 2......Page 193
9 Graphs in surfaces......Page 202
Regular neighbourhoods......Page 205
Surfaces......Page 209
Lefschetz duality......Page 213
A three-dimensional situation......Page 217
Separating surfaces by graphs......Page 220
Representation of homology elements by simple closed polygons......Page 222
Orientation preserving and reversing loops......Page 225
A generalization of Euler’s formula......Page 229
Brussels Sprouts......Page 233
Basic definitions......Page 237
Finitely generated (f.g.) and free abelian groups......Page 239
Quotient groups......Page 241
Exact sequences......Page 243
Direct sums and splitting......Page 244
Presentations......Page 248
Rank of a f.g. abelian group......Page 255
Books......Page 261
Articles in journals and books......Page 262
Index......Page 265