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Previous Title:	Fomenko, Anatolij Timofeevič: Homotopic topology
Main Authors:	Fomenko, Anatolij Timofeevič 1945- (Author), Fuks, Dmitrij B. 1939- (Author)
Format:	Electronic eBook
Language:	English
Published:	Cham Springer [2016]
Edition:	Second edition
Series:	Graduate Texts in Mathematics 273
Subjects:	Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Algebraic Topology Mathematik Homotopietheorie Topologie
Online Access:	BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Inhaltsverzeichnis
Physical Description:	1 Online-Ressource (XI, 627 Seiten, 210 illus)
ISBN:	9783319234885
ISSN:	0072-5285
DOI:	10.1007/978-3-319-23488-5

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adam_text	Titel: Homotopical topology Autor: Fomenko, Anatolij Timofeevič Jahr: 2016 Contents Introduction: The Most Important Topological Spaces...................... I Lecture 1. Classical Spaces.................................................. 1 Lecture 2. Basic Operations over Topological Spaces...................... 16 Chapter 1. Homotopy ......................................................... 25 Lecture 3. Homotopy and Homotopy Equivalence......................... 25 Lecture 4. Natural Group Structures in the Sets n(X, Y) ................... 33 Lecture 5. CW Complexes................................................... 38 Lecture 6. The Fundamental Group and Coverings......................... 60 Lecture 7. Van Kampen’s Theorem and Fundamental Groups of CW Complexes................................................ 79 Lecture 8. Homotopy Groups................................................ 93 Lecture 9. Fibrations ......................................................... 104 Lecture 10. The Suspension Theorem and Homotopy Groups of Spheres......................................................... 121 Lecture 11. Homotopy Groups and CW Complexes......................... 129 Chapter 2. Homology............ 143 Lecture 12. Main Definitions and Constructions............................. 143 Lecture 13. Homology of CW Complexes.................................... 158 Lecture 14. Homology and Homotopy Groups............................... 178 Lecture 15. Homology with Coefficients and Cohomology................. 183 Lecture 16. Multiplications.................................................... 203 Lecture 17. Homology and Manifolds........................................ 215 Lecture 18. The Obstruction Theory.......................................... 253 Lecture 19. Vector Bundles and Their Characteristic Classes............... 270 Chapter 3. Spectral Sequences of Fibrations ............................... 305 Lecture 20. An Algebraic Introduction....................................... 305 Lecture 21. Spectral Sequences of a Filtered Topological Space............ 321 Lecture 22. Spectral Sequences of Fibrations: Definitions and Basic Properties.............................................. 324 Lecture 23. Additional Properties of Spectral Sequences of Fibrations ..... 336 IX X Contents Lecture 24. A Multiplicative Structure in a Cohomological Spectral Sequence ................................................ 349 Lecture 25. Killing Spaces Method for Computing Homotopy Groups..... 364 Lecture 26. Rational Cohomology of K(jt, n) and Ranks of Homotopy Groups............................................. 367 Lecture 27. Odd Components of Homotopy Groups......................... 379 Chapter 4. Cohomology Operations......................................... 389 Lecture 28. General Theory................................................... 389 Lecture 29. Steenrod Squares................................................. 395 Lecture 30. The Steenrod Algebra............................................ 401 Lecture 31. Applications of Steenrod Squares ............................... 414 Chapter 5. The Adams Spectral Sequence.................................. 429 Lecture 32. General Idea...................................................... 429 Lecture 33. The Necessary Algebraic Material............................... 434 Lecture 34. The Construction of the Adams Spectral Sequence............. 444 Lecture 35. Multiplicative Structures......................................... 463 Lecture 36. An Application of the Adams Spectral Sequence to Stable Homotopy Groups of Spheres......................... 472 Lecture 37. Partial Cohomology Operation .................................. 487 Chapter 6. A-Theory and Other Extraordinary Cohomology Theories............................................ 495 Lecture 38. General Theory................................................... 495 Lecture 39. Calculating K-Functor: Atiyah-Hirzebruch Spectral Sequence 516 Lecture 40. The Adams Operations....................................... 525 Lecture 4L J-functor........................................................... 533 Lecture 42. The Riemann-Roch Theorem.................................... 551 Lecture 43. The Atiyah-Singer Formula: A Sketch.......................... 577 Lecture 44. Cobordisms....................................................... 584 Captions for the Illustrations................................................... 605 References......................................................................... 613 Name Index....................................................................... 619 Subject Index 623
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spelling	Fomenko, Anatolij Timofeevič 1945- Verfasser (DE-588)119092689 aut Gomotopičeskaja topologija Homotopical topology Anatoly Fomenko, Dmitry Fuchs Second edition Cham Springer [2016] 1 Online-Ressource (XI, 627 Seiten, 210 illus) txt rdacontent c rdamedia cr rdacarrier Graduate texts in mathematics 273 0072-5285 Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Algebraic Topology Mathematik Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 Homotopietheorie (DE-588)4128142-1 s Fuks, Dmitrij B. 1939- Verfasser (DE-588)110261984 aut Erscheint auch als Druckausgabe 978-3-319-23487-8 Vorangegangen ist Frühere Ausgabe Fomenko, Anatolij Timofeevič: Homotopic topology Graduate Texts in Mathematics 273 (DE-604)BV035421258 273 https://doi.org/10.1007/978-3-319-23488-5 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029063924&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Fomenko, Anatolij Timofeevič 1945- Fuks, Dmitrij B. 1939- Homotopical topology Graduate Texts in Mathematics Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Algebraic Topology Mathematik Homotopietheorie (DE-588)4128142-1 gnd Topologie (DE-588)4060425-1 gnd
subject_GND	(DE-588)4128142-1 (DE-588)4060425-1
title	Homotopical topology
title_alt	Gomotopičeskaja topologija
title_auth	Homotopical topology
title_exact_search	Homotopical topology
title_full	Homotopical topology Anatoly Fomenko, Dmitry Fuchs
title_fullStr	Homotopical topology Anatoly Fomenko, Dmitry Fuchs
title_full_unstemmed	Homotopical topology Anatoly Fomenko, Dmitry Fuchs
title_old	Fomenko, Anatolij Timofeevič: Homotopic topology
title_short	Homotopical topology
title_sort	homotopical topology
topic	Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Algebraic Topology Mathematik Homotopietheorie (DE-588)4128142-1 gnd Topologie (DE-588)4060425-1 gnd
topic_facet	Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Algebraic Topology Mathematik Homotopietheorie Topologie
url	https://doi.org/10.1007/978-3-319-23488-5 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029063924&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV035421258
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MARC

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