This monograph is for a unified theory of surfaces， embeddings and maps all considered as polyhedra via the joint tree modal which was initiated from the author's articles in the seventies of last century and has been basically developed in recent decades. Complete invariants for each classification are topologically， combinatorially or isomorphically extracted. A number of counting polynomials including handle and crosscap polynomials are presented. In particular， an appendix serves as the exhaustive counting super maps （rooted and nonrooted） including these polynomials with under graphs of small size for the reader's digests.Although the book is mainly for researchers in mathematics， theoretical physics， chemistry， biology and some others related， the basic part in each chapter can also be chosen for graduates and college teachers as references.
作者簡介
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圖書目錄
Preface Chapter Ⅰ Preliminaries Ⅰ.1 Sets and mappings Ⅰ.2 Partitions and permutations Ⅰ.3 Group actions Ⅰ.4 Networks Ⅰ.5 Notes Chapter Ⅱ Surfaces Ⅱ.1 Polyhedra Ⅱ.2 Elementary equⅣalence Ⅱ.3 Polyhegons Ⅱ.4 Orientability Ⅱ.5 Classification Ⅱ.6 Notes Chapter Ⅲ Embeddings of Graphs Ⅲ.1 Geometric consideration Ⅲ.2 Surface closed curve axiom Ⅲ.3 Distinction Ⅲ.4 Joint tree model Ⅲ.5 Combinatorial properties Ⅲ.6 Notes Chapter Ⅳ Mathematical Maps Ⅳ.1 Basic permutations Ⅳ.2 Conjugate axiom Ⅳ.3 TransitⅣity Ⅳ.4 Included angles Ⅳ.5 Notes Chapter Ⅴ Duality on Surfaces Ⅴ.1 Dual partition of edges Ⅴ.5 Notes Chapter Ⅵ Invariants on Basic Class Ⅵ.1 Orientability Ⅵ.2 Euler characteristic Ⅵ.3 Basic equⅣalence Ⅵ.4 Orientable maps Ⅵ.5 Nonorientable maps Ⅵ.6 Notes Chapter Ⅶ Asymmetrization Ⅶ.1 Isomorphisms Ⅶ.2 Recognition Ⅶ.3 Upper bound of group order Ⅶ.4 Determination of the group Ⅶ.5 Rootings Ⅶ.6 Notes Chapter Ⅷ Asymmetrized Census Ⅷ.1 Orientable equation Ⅷ.2 Planar maps... Ⅷ.3 Nonorientable equation Ⅷ.4 Gross equation Ⅷ.5 The number of maps Ⅷ.6 Notes Chapter Ⅸ Petal Bundles Ⅸ.1 Orientable petal bundles Ⅸ.2 Planar pedal bundles Ⅸ.3 Nonorientable pedal bundles Ⅸ.4 The number of pedal bundles Ⅸ.5 Notes Chapter Ⅹ Super Maps of Genus Zero Chapter Ⅺ Symmetric Census Chapter Ⅻ Cycle Oriented Maps Chapter ⅫⅠ Census by Genus Chapter ⅩⅣ Classic Applications Appendix Ⅰ Embeddings and maps of Small Size Distributed by Genus Appendix Ⅱ Orientable Forms of Surfaces and Their Nonorientable Genus Polynomials Bibliography Subject Index Author Index
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