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Homotopical topology /

Fomenko, Anatoly T.

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Homotopical topology /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Homotopical topology // Anatoly Fomenko, Dmitry Fuchs.
作者:	Fomenko, Anatoly T.
其他作者:	Fuks, Dmitry B.
出版者:	Switzerland :Springer International Publishing, : c2016.,
面頁冊數:	xi, 627 p. :ill. ;25 cm.
附註:	"© Moscow University Press 1969 (first edition in Russian); © Akadémiai Kiadó 1989 (first edition in English)"--Title page verso.
標題:	Homotopy theory. -
ISBN:	9783319234878
ISSN:	0072-5285

Homotopical topology /
Fomenko, Anatoly T.

Homotopical topology /Anatoly Fomenko, Dmitry Fuchs. - 2nd ed. - Switzerland :Springer International Publishing,c2016. - xi, 627 p. :ill. ;25 cm. - Graduate texts in mathematics,2730072-5285 ;. - Graduate texts in mathematics ;273..

"© Moscow University Press 1969 (first edition in Russian); © Akadémiai Kiadó 1989 (first edition in English)"--Title page verso.

Includes bibliographical references (p. 613-617) and indexes.

Introduction : The most important topological spaces --

"This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics--the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homologyand cohomology, homological algebra--the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements ofthe golden era of topology--the Adams conjecture, Bott periodicity, the Hirzebruch-Riemann-Roch theorem, the Atiyah-Singer index theorem, to name a few--paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail,enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up thereader's mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanicsof spectral sequences and other sophisticated methods. Over fiftyhauntingly captivating images by A.T. Fomenko artistically renderthe wondrous beauty, and mystery, of the subject"-- Page 4 of cover.

ISBN: 9783319234878EUR69.99

ISSN: 0072-5285Subjects--Topical Terms:

604501
Homotopy theory.

LC Class. No.: QA612.7 / .F8513 2016

Dewey Class. No.: 514.24

Homotopical topology /
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020 $a 9783319234878 $q (hbk.) : $c EUR69.99
020 $a 3319234870 $q (hbk.)
020 $a 9783319234885 $q (ebk.)
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022 $a 0072-5285
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082 0 4 $a 514.24 $2 23
100 1 $a Fomenko, Anatoly T. $3 3167332
240 1 0 $a Gomotopicheskai︠a︡ topologii︠a︡. $l English
245 1 0 $a Homotopical topology / $c Anatoly Fomenko, Dmitry Fuchs.
250 $a 2nd ed.
260 # $a Switzerland : $b Springer International Publishing, $c c2016.
300 $a xi, 627 p. : $b ill. ; $c 25 cm.
490 1 0 $a Graduate texts in mathematics, $x 0072-5285 ; $v 273
500 $a "© Moscow University Press 1969 (first edition in Russian); © Akadémiai Kiadó 1989 (first edition in English)"--Title page verso.
504 $a Includes bibliographical references (p. 613-617) and indexes.
505 0 # $t Introduction : The most important topological spaces -- $t Homotopy -- $t Homology -- $t Spectral sequences of fibrations -- $t Cohomology operations -- $t The Adams spectral sequence -- $t K-theory and other extraordinary cohomology theories.
520 # $a "This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics--the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homologyand cohomology, homological algebra--the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements ofthe golden era of topology--the Adams conjecture, Bott periodicity, the Hirzebruch-Riemann-Roch theorem, the Atiyah-Singer index theorem, to name a few--paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail,enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up thereader's mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanicsof spectral sequences and other sophisticated methods. Over fiftyhauntingly captivating images by A.T. Fomenko artistically renderthe wondrous beauty, and mystery, of the subject"-- Page 4 of cover.
650 # 0 $a Homotopy theory. $3 604501
650 # 0 $a Topological algebras. $3 725781
700 1 # $a Fuks, Dmitry B. $3 3167333
830 0 $a Graduate texts in mathematics ; $v 273. $3 3166108