圖的拓?fù)淅碚?/h1>

出版時(shí)間：2008-9  出版社：中國(guó)科學(xué)技術(shù)大學(xué)出版社  作者：劉彥佩  頁(yè)數(shù)：458  
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前言

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(chǎn) graph is only a 1-complex without two cells．

內(nèi)容概要

　　本書不在于圖的拓?fù)湫再|(zhì)本身，而是著意以圖為代表的一些組合構(gòu)形為出發(fā)點(diǎn)，揭示與拓?fù)鋵W(xué)中一些典型對(duì)蠏，如多面形、曲面、嵌入、紐結(jié)等的聯(lián)系，特別是顯示了定理有效化的途徑對(duì)于以拓?fù)鋵W(xué)為代表的基礎(chǔ)數(shù)學(xué)的作用。同時(shí)，也提出了一些新的曲面模型，為超大規(guī)模集成電路的布線嘗試構(gòu)建多方面的理論基礎(chǔ)?！　”緯勺鳛榛A(chǔ)數(shù)學(xué)，應(yīng)用數(shù)學(xué)、系統(tǒng)科學(xué)、計(jì)算機(jī)科學(xué)等專業(yè)高年級(jí)本科生和研究生的補(bǔ)充教材，也可供相關(guān)專業(yè)的教師和科研工作者參考。

書籍目錄

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

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《圖的拓?fù)淅碚摗房勺鳛榛A(chǔ)數(shù)學(xué)，應(yīng)用數(shù)學(xué)、系統(tǒng)科學(xué)、計(jì)算機(jī)科學(xué)等專業(yè)高年級(jí)本科生和研究生的補(bǔ)充教材，也可供相關(guān)專業(yè)的教師和科研工作者參考。

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