图的拓扑理论
2008-9
中国科学技术大学出版社
刘彦佩
458
无
The subject of this book reflects new developments mainly by theauthor himself in company with cooperators most of them his formerand present graduate students on the foundation established in Liu，Y．P．[33-34]．The central idea iS to extract suitable parts of a topo-logical obj ect such a8 a graph not necessary to be with symmetry,aslinear spaces which are all with symmetry for exploiting global proper-ties in construction of the object．This iS a way of combinatorizationsand further algebraications of an obj ect via relationship among theirsubspaces． Graphs are dealt with three vector spaces over GF（2），the finitefield of order 2，generated by O（dimensional）-cells，1（dimensional）-cellsand 2（dimensional）-cells．The first two spaces were known from，e．g．，Lefschetz，S．[2] by taking O-cells and 1-cells as，respectively，vertices and edges．Of course．a graph is only a 1-complex without two cells．
本书不在于图的拓扑性质本身，而是着意以图为代表的一些组合构形为出发点，揭示与拓扑学中一些典型对蠏，如多面形、曲面、嵌入、纽结等的联系，特别是显示了定理有效化的途径对于以拓扑学为代表的基础数学的作用。同时，也提出了一些新的曲面模型，为超大规模集成电路的布线尝试构建多方面的理论基础。 本书可作为基础数学，应用数学、系统科学、计算机科学等专业高年级本科生和研究生的补充教材，也可供相关专业的教师和科研工作者参考。
PrefaceChapter 1 Preliminaries 1.1 Sets and relations 1.2 Partitions and permutations 1.3 Graphs and networks 1.4 Groups and spaces 1.5 NotesChapter 2 Polyhedra 2.1 Polygon double covers 2.2 Supports and skeletons 2.3 Orientable polyhedra 2.4 Nonorientable polyhedra 2.5 Classic polyhedra 2.6 NotesChapter 3 Surfaces 3.1 Polyhegons 3.2 Surface closed curve axiom 3.3 Topological transformations 3.4 Complete invariants 3.5 Graphs on surfaces 3.6 Up-embeddability 3.7 NotesChapter 4 Homology on Polyhedra 4.1 Double cover by travels 4.2 Homology 4.3 Cohomology 4.4 Bicycles 4.5 NotesChapter 5 Polyhedra on the Sphere 5.1 Planar polyhedra 5.2 Jordan closed curve axiom 5.3 Uniqueness 5.4 Straight line representations 5.5 Convex representation 5.6 NotesChapter 6 Automorphisms of a Polyhedron 6.1 Automorphisms 6.2 V-codes and F-codes 6.3 Determination of automorphisms 6.4 Asymmetrization 5.5 NotesChapter 7 Gauss Crossing Sequences 7.1 Crossing polyhegons 7.2 Dehn's transformation 7.3 Algebraic principles 7.4 Gauss Crossing problem 7.5 NotesChapter 8 Cohomology on Graphs 8.1 Immersions 8.2 Realization of planarity 8.3 Reductions 8.4 Planarity auxiliary graphs 8.5 Basic conclusions 8.6 Notes ……Chapter 9 Embeddability on SurfacesChapter 10 Embeddings on the SphereChapter 11 Orthogonality on SurfacesChapter 12 Net EmbeddingsChapter 13 Extremality on SurfacesChapter 14 Matroial GraphicnessChapter 15 Knot PolynomialsBibliographySubject IndexAuthor Index
插图：
《图的拓扑理论》可作为基础数学，应用数学、系统科学、计算机科学等专业高年级本科生和研究生的补充教材，也可供相关专业的教师和科研工作者参考。
无