[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-272672-105":59,"doc-detail-272672-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","algebraic-topology-readable-introduction","Algebraic Topology - Readable Introduction","","A readable introduction to algebraic topology provides broad coverage from classical geometric viewpoints. The material is organized around four chapters separating the two central channels: homology and homotopy, with cohomology as the mirror variant. Homotopy ideas concentrate in Chapters 1 and 4, while homology and cohomology appear in Chapters 2 and 3, with an optional perspective linking them as branches of homotopy theory. A preliminary Chapter 0 develops key geometric constructions, emphasizing CW complexes and intuition.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":15,"@type":76,"position":81},"https://docshare.wps.com/document/literature/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/algebraic-topology-readable-introduction/272672/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/algebraic-topology-readable-introduction/272672.png","ImageObject",300,407,{"name":92,"@type":93},"Theodora","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is the book organized across homology and homotopy topics?","Question",{"text":112,"@type":113},"The content is split into four chapters: homotopy is covered in Chapters 1 and 4, while homology and cohomology appear in Chapters 2 and 3.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the role of the preliminary Chapter 0?",{"text":117,"@type":113},"Chapter 0 introduces underlying geometric notions and constructions that support both the homological and homotopical sides of the subject.",{"name":119,"@type":110,"acceptedAnswer":120},"Why does the book emphasize CW complexes?",{"text":121,"@type":113},"CW complexes are described as the most natural class of spaces for algebraic topology, so they receive stronger emphasis than in earlier generations of books.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},272672,1790816360,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":14,"category_name":15,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},687197207919,"https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552","Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix  \nStandard Notations xii.  \nChapter 0. Some Underlying Geometric Notions . . . . . 1 Homotopy and Homotopy Type 1 . Cell Complexes 5 .  \nOperations on Spaces 8 . Two Criteria for Homotopy Equivalence 10 .  \nThe Homotopy Extension Property 14 .  \nChapter 1. The Fundamental Group ............. 21  \n1.1. Basic Constructions ..................... 25  \nPaths and Homotopy 25 . The Fundamental Group of the Circle 29 .  \nInduced Homomorphisms 34 .  \n1.2. Van Kampen’s Theorem ................... 40  \nFree Products of Groups 41 . The van Kampen Theorem 43 .  \nApplications to Cell Complexes 49 .  \n1.3. Covering Spaces ........................ 56  \nLifting Properties 60 . The Classi􀀌cation of Covering Spaces 63 .  \nDeck Transformations and Group Actions 70 .  \nAdditional Topics  \n1.A. Graphs and Free Groups 83 .  \n1.B. K(G,1) Spaces and Graphs of Groups 87 .  \nChapter 2. Homology ....................... 97  \n2.1. Simplicial and Singular Homology ............. 102  \n∆  Complexes 102 . Simplicial Homology 104 . Singular Homology 108.  \nHomotopy Invariance 110 . Exact Sequences and Excision 113 .  \nThe Equivalence of Simplicial and Singular Homology 128 .  \n2.2. Computations and Applications .............. 134  \nDegree 134 . Cellular Homology 137 . Mayer-Vietoris Sequences 149 .  \nHomology with Coe􀀎cients 153 .  \n2.3. The Formal Viewpoint .................... 160  \nAxioms for Homology 160 . Categories and Functors 162 .  \nAdditional Topics  \n2.A. Homology and Fundamental Group 166 .  \n2.B. Classical Applications 169 .  \n2.C. Simplicial Approximation 177 .  \nChapter 3. Cohomology ..................... 185  \n3.1. Cohomology Groups ..................... 190  \nThe Universal Coe􀀎cient Theorem 190 . Cohomology of Spaces 197.  \n3.2. Cup Product .......................... 206  \nThe Cohomology Ring 212 . A K¨unneth Formula 214 .  \nSpaces with Polynomial Cohomology 220 .  \n3.3. Poincar Duality ........................ 230  \nOrientations and Homology 233 . The Duality Theorem 239 .  \nConnection with Cup Product 249 . Other Forms of Duality 252 .  \nAdditional Topics  \n3.A. Universal Coe􀀎cients for Homology 261 .  \n3.B. The General K¨unneth Formula 268 .  \n3.C. H–Spaces and Hopf Algebras 281 .  \n3.D. The Cohomology of SO(n) 292 .  \n3.E. Bockstein Homomorphisms 303 .  \n3.F. Limits and Ext 311 .  \n3.G. Transfer Homomorphisms 321 .  \n3.H. Local Coe􀀎cients 327 .  \nChapter 4. Homotopy Theory ................. 337  \n4.1. Homotopy Groups ...................... 339  \nDe􀀌nitions and Basic Constructions 340 . Whitehead’s Theorem 346 .  \nCellular Approximation 348 . CW Approximation 352 .  \n4.2. Elementary Methods of Calculation ............ 360  \nExcision for Homotopy Groups 360 . The Hurewicz Theorem 366 .  \nFiber Bundles 375 . Stable Homotopy Groups 384 .  \n4.3. Connections with Cohomology .............. 393  \nThe Homotopy Construction of Cohomology 393 . Fibrations 405.  \nPostnikov Towers 410 . Obstruction Theory 415 .  \nAdditional Topics  \n4.A. Basepoints and Homotopy 421 .  \n4.B. The Hopf Invariant 427 .  \n4.C. Minimal Cell Structures 429 .  \n4.D. Cohomology of Fiber Bundles 431 .  \n4.E. The Brown Representability Theorem 448 .  \n4.F. Spectra and Homology Theories 452 .  \n4.G. Gluing Constructions 456 .  \n4.H. Eckmann-Hilton Duality 460 .  \n4.I. Stable Splittings of Spaces 466 .  \n4.J. The Loopspace of a Suspension 470 .  \n4.K. The Dold-Thom Theorem 475 .  \n4.L. Steenrod Squares and Powers 487 .  \nAppendix ............................... 519  \nTopology of Cell Complexes 519 . The Compact-Open Topology 529.  \nThe Homotopy Extension Property 533 . Simplicial CW Structures 534 .  \nBibliography .............................. 540  \nIndex ................................... 546  \nThis book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in spirit, and stays well within the con􀀌nes of pure algebrai","cbCaijNLcRytlFQb","https://ap.wps.com/l/cbCaijNLcRytlFQb","pdf",8121741,560,"English","# Chapter 0. Some Underlying Geometric Notions\n## Homotopy and Homotopy Type\n## Operations on Spaces\n## Two Criteria for Homotopy Equivalence\n## The Homotopy Extension Property\n# Chapter 1. The Fundamental Group\n## Basic Constructions\n## Van Kampen’s Theorem\n## Covering Spaces\n# Chapter 2. Homology\n## Simplicial and Singular Homology\n## Computations and Applications\n## The Formal Viewpoint\n# Chapter 3. Cohomology\n## Cohomology Groups\n## Cup Product\n## Poincaré Duality\n# Chapter 4. Homotopy Theory\n## Homotopy Groups\n## Elementary Methods of Calculation\n## Connections with Cohomology\n# Appendix","[{\"question\":\"How is the book organized across homology and homotopy topics?\",\"answer\":\"The content is split into four chapters: homotopy is covered in Chapters 1 and 4, while homology and cohomology appear in Chapters 2 and 3.\"},{\"question\":\"What is the role of the preliminary Chapter 0?\",\"answer\":\"Chapter 0 introduces underlying geometric notions and constructions that support both the homological and homotopical sides of the subject.\"},{\"question\":\"Why does the book emphasize CW complexes?\",\"answer\":\"CW complexes are described as the most natural class of spaces for algebraic topology, so they receive stronger emphasis than in earlier generations of books.\"}]","Algebraic Topology - Readable Introduction | PDF",1789466898,862]