代數拓撲導論 [Algebraic Topology:An Introduction] 下載 mobi epub pdf 電子書 2024

☆☆☆☆☆
簡體網頁||繁體網頁



點擊這裡下載

類似圖書 點擊查看全場最低價

---

內容簡介

This textbook is designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as possible. The principal topics treated are 2-dimensional manifolds， the fundamental group， and covering spaces， plus the group theory needed in these topics. The only prerequisites are some group theory， such as that normally contained in an undergraduate algebra course on the junior-senior level， and a one-semester undergraduate course in general topology.
The topics discussed in this book are "standard" in the sense that several well-known textbooks and treatises devote a few sections or a chapter to them. This， I believe， is the first textbook giving a straightforward treatment of these topics， stripped of all unnecessary definitions， terminology， etc.， and with numerous examples and exercises， thus making them intelligible to advanced undergraduate students.

內頁插圖

目錄

CHAPTERONETwo-DimensionalManifolds
1 Introduction
2 Definitionandexamplesofn-manifolds
3 Orientablevs.nonorientablemanifolds
4 Examplesofcompact，connected2-manifolds
5 Statementoftheclassificationtheoremforcompactsurfaces
6 Triangulationsofcompactsurfaces
7 ProofofTheorem5.1
8 TheEulercharacteristicofasurface
9 Manifoldswithboundary
10 Theclassificationofcompact，connected2-manifoldswithboundary
11 TheEulercharacteristicofaborderedsurface
12 ModelsofcompactborderedsurfacesinEuclidean3-space
13 Remarksonnoncompactsurfaces

CHAPTERTWOTheFundamentalGroup
1 Introduction
2 Basicnotationandterminology
3 Definitionofthefundamentalgroupofaspace
4 Theeffectofacontinuousmai)pingonthefundamentalgroup
5 Thefundamentalgroupofacircleisinfinitecyclic
6 Application：TheBrouwerfixed-pointtheoremilldimension2
7 Thefundamentalgroupofaproductspace
8 Homotopytypeandhomotopyequivalenceofspaces

CHAPTERTHREEFreeGroupsandFreeProductsofGroups
1 Introduction
2 Theweakproductofabeliangroups
3 Freeabeliangroups
4 Freeproductsofgroups
5 Freegroups
6 Thepresentationofgroupsbygeneratorsandrelations
7 Universalmappingproblems

CHAPTERFOURScifertandVanKampenTheoremontheFundamentalGroupoftheUnionofTwoSpaces.Applic
ations
1 Introduction
2 StatementandproofofthetheoremofSeifertandVanKampen
3 FirstapplicationofTheorem2.1
4 SecondapplicationofTheorem2.1
5 Structureofthefundamentalgroupofacompactsurface
6 Applicationtoknottheory

CHAPTERFIVECoveringSpaces
1 Introduction
2 Definitionandsomeexamplesofcoveringspaces
3 Liftingofpathstoacoveringspace
4 Thefundamentalgroupofacoveringspace
5 Liftingofarbitrarymapstoacoveringspace
6 Homomorphismsandautomorphismsofcoveringspaces
7 Theactionofthegroupπ(X，x)onthesetp-(x)
8 Regularcoveringspacesandquotientspaces
9 Application：TheBorsuk-Ulamtheoremforthe2-sphere
10 Theexistencetheoremforcoveringspaces
11 Theinducedcoveringspaceoverasubspace
12 Pointsettopologyofcoveringspaces

CHAPTERSIXTheFundamentalGroupandCoveringSpacesofaGraph.ApplicationstoGroupTheory
1 Introduction
2 Definitionandexamples
3 Basicpropertiesofgraphs
4 Trees
5 Thefundamentalgroupofagraph
6 TheEulercharacteristicofafinitegraph
7 Coveringspacesofagraph
8 Generatorsforasubgroupoffreegroup

CHAPTERSEVENTheFundamentalGroupofHigherDimensionalSpaces
1 Introduction
2 Adjunctionof2-cellstoaspace
3 Adjunctionofhigherdimensionalcellstoaspace
4 CW-complexes
5 TheKuroshsubgrouptheorem
6 GrushkosTheorem

CHAPTEREIGHTEpilogue
APPENDIXATheQuotientSpaceorIdentificationSpaceTopology
1 Definitionsandbasicproperties
2 Ageneralizationofthequotientspacetopology
3 Quotientspacesandproductspaces
4 Subspaceofaquotientspacevs.quotientspaceofasubspace
5 ConditionsforaquotientspacetobeaHausdorffspace

APPENDIXBPermutationGroupsorTransformationGroups
1 Basicdefinitions
2 HomogeneousG-spaces
Index

前言/序言

　　This textbook iS designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as pos- sible.The principal topics treated are 2.dimcnsional manifolds.the fundamental group，and covering spaces，plus the group theory needed in these topics.The only prerequisites are some group theory，such as that normally centained jn an undergraduate algebra course on the junior-senior level，and a one·semester undergraduate course in general topology.
　　The topics discussed in this book are“standard”in the sense that several well-known textbooks and treatises devote a fey.r sections or a chapter to them.This。I believe，iS the first textbook giving a straight- forward treatment of these topics。stripped of all unnecessary definitions， terminology，etc.，and with numerous examples and exercises，thus making them intelligible to advanced undergraduate students.
　　The SUbject matter i8 used in several branches of mathematics other than algebraic topology，such as differential geometry，the theory of Lie groups，the theory of Riemann surfaces。or knot theory.In the develop- merit of the theory，there is a nice interplay between algebra and topology which causes each to reinfoFee interpretations of the other.Such an interplay between different topics of mathematics breaks down the often artificial subdivision of mathematics into difierent“branches”and emphasizes the essential unity of all mathematics.

代數拓撲導論 [Algebraic Topology:An Introduction] 下載 mobi epub pdf txt 電子書 格式

評分☆☆☆☆☆

印刷很好

評分☆☆☆☆☆

好吧

評分☆☆☆☆☆

印刷不夠好。

評分☆☆☆☆☆

印刷很好

評分☆☆☆☆☆

印刷很好

評分☆☆☆☆☆

印刷不夠好。

評分☆☆☆☆☆

給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆

評分☆☆☆☆☆

很基礎的書，應該不錯，期待代數拓撲學好

評分☆☆☆☆☆

很好…………

類似圖書 點擊查看全場最低價