吳文俊全集拓?fù)鋵W(xué)卷II

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作　者：	吳文俊
出版社：	科學(xué)出版社
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標(biāo)　簽：	暫缺

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ISBN：	9787508855585	出版時(shí)間：	2019-05-01	包裝：	精裝
開本：	16開	頁數(shù)：	291	字?jǐn)?shù)：

內(nèi)容簡(jiǎn)介

　　本卷收錄了吳文俊的A Theory of Imbedding，Immersion，and Isotopy of Polytopes in a Euclidean Space一書。一個(gè)空間嵌入另一空間（例如歐氏空間）是否可能以及這些嵌入所依據(jù)的同痕的分類問題，已成為拓?fù)鋵W(xué)中重要的中心問題之一，也是許多拓?fù)鋵W(xué)家從各種不同角度用各種不同方法研究的對(duì)象之一。《吳文俊全集·拓?fù)鋵W(xué)卷II》是作者從1954年以來在這方面研究工作的一個(gè)總結(jié)報(bào)告，它的方法在于研究空間的去核p重積，即將p重積除去對(duì)角以后所余的空間，這一概念可追溯到Van Kampen早在1932年的一篇重要論文。其次再應(yīng)用P.A.Smith有關(guān)周期變換的理論以獲得若干作為Smith特殊群中上類的不變量，它們之為0是嵌入的必要條件而在某些極端情形又同時(shí)為充分條件。關(guān)于嵌入的許多已知結(jié)果以及一些新的結(jié)果，雖有著種種不同的來源，都可用這一統(tǒng)一的方法得出。浸入與同痕也可用同樣辦法處理并得出相應(yīng)的類似結(jié)果。

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暫缺《吳文俊全集拓?fù)鋵W(xué)卷II》作者簡(jiǎn)介

圖書目錄

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)