本卷收录了吴文俊的A Theory of Imbedding，Immersion，and Isotopy of Polytopes in a Euclidean Space一书。一个空间嵌入另一空间（例如欧氏空间）是否可能以及这些嵌入所依据的同痕的分类问题，已成为拓扑学中重要的中心问题之一，也是许多拓扑学家从各种不同角度用各种不同方法研究的对象之一。本书是作者从1954年以来在这方面研究工作的一个总结报告，它的方法在于研究空间的去核p重积，即将p重积除去对角以后所余的空间，这一概念可追溯到Van Kampen早在1932年的一篇重要论文。其次再应用P.A.Smith有关周期变换的理论以获得若干作为Smith特殊群中上类的不变量，它们之为0是嵌入的必要条件而在某些极端情形又同时为充分条件。关于嵌入的许多已知结果以及一些新的结果，虽有着种种不同的来源，都可用这一统一的方法得出。浸入与同痕也可用同样办法处理并得出相应的类似结果。
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目录
Contents §1 The Problem of realization or imbedding (iii) §2 Analysis of some known methods (iii) §3 Method of this book (ix) §4 Structure of the book (xii) CHAPTER I TOPOLOGICAL INVARIANTS OF NON-HOMOTOPIC TYPE OF A FINITE POLYTOPE (1) §1 The notion of complexes (1) §2 Regular pairs of complexes and polytopes (9) §3 Topological invariants of regular pairs of finite polytopes (12) §4 Regular pairs associated to a finite polytope (21) §5 Remarks (28) CHAPTER II THEORY OF P A SMITH ABOUT SPACES UNDER PERIODIC TRANSFORMATIONS WITH No FIXED POINTS 35) §1 Complexes with transformation groups (35) §2 Complexes under periodic transformations (44) §3 Smith homomorphisms and their properties (58) §4 Spaces with transformation groups (71) CHAPTER III A GENERAL METHOD FOR THE STUDY OF IMBEDDING, IMMERSION AND ISOTOPY (92) §1 Fundamental concepts (92) §2 The * and * -classes of a finite polytope (101) §3 Examples (112) §4 Isotopy and isoposition (121) CHAPTER IV CONDITIONS OF IMBEDDING AND IMMERSION IN TERMS OF CoHOMOLOGY OPERATIONS (128) §1 Smith theory of complexes under periodic transformations with invariant subcomplexes (128) §2 Special homologies in product complexes (140) §3 Smith operations (153) §4 Conditions of imbedding and immersion in terms of smith operations (162) §5 Relations between smith operations and steenrod powers (166) CHAPTER V THEORY OF OBSTRUCTIONS FOR THE IMBEDDING IMMERsmN AND IsoTOPY OF COMPLEXES IN A EucLIDEAN SPACE (172) §1 Linear realization of a complex in a euclidean space (172) §2 Intersections and linkings in euclidean spaces (175〉 §3 Obstruction to imbeddings of a complex in Euclidean spaces (181) §4 The realization of a cocycle in the imbedding class as an imbedding cocycle (186) §5 The coincidence of imbedding classes * with the * -classes * of a finite simplicial complex K (190) §6 Obstruction to immersion of a complex in a Euclidean space (196) §7 Obstruction to isotopy of imbeddings in a Euclidean space (198) CHAPTER VI SUFFICIENCY THEOREMS FOR THE IMBEDDING IMMERsmN, AND IsoTOPY IN A EucLmEAN SPACE (208) §1 Some elementary sufficiency theorems (208) §2 Some fundamentals about C∞-maps (212) §3 Some auxiliary geometric constructions (223) §4 The main theorem for imbedding-necessary and sufficient conditions for Kn*R2n n>2 (233) §5 The main theorem for immersion-necessary and sufficient condition for Kn*R2n-1 n>3 (239) §6 The main theorem for isotopy-necessary and sufficient conditions for f,g: Kn*R2n+1，n>1 to be isotopic (243) CHAPTER VII IMBEDDING IMMERSION AND ISOTOPY OF MANIFOLDS IN A EUCLIDEAN SPACE (252) §1 Periodic transformations in combinatorial manifolds (252) §2 Sufficiency theorems for combinatorial manifolds (255) §3 Imbedding of a combinatorial manifold (259) §4 Immersion of a combinatorial manifold (266) §5 An extension of the general theory in the case of differential manifolds (274) Bibliographical Notes (283) Bibliography (288)
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