000 03246nam a22004335i 4500
001 978-1-4419-7329-0
003 DE-He213
005 20140220083723.0
007 cr nn 008mamaa
008 110714s2011 xxu| s |||| 0|eng d
020 _a9781441973290
_9978-1-4419-7329-0
024 7 _a10.1007/978-1-4419-7329-0
_2doi
050 4 _aQA612-612.8
072 7 _aPBPD
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514.2
_223
100 1 _aArkowitz, Martin.
_eauthor.
245 1 0 _aIntroduction to Homotopy Theory
_h[electronic resource] /
_cby Martin Arkowitz.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aXIII, 344 p. 333 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _a1 Basic Homotopy -- 2 H-Spaces and Co-H-Spaces -- 3 Cofibrations and Fibrations -- 4 Exact Sequences -- 5 Applications of Exactness -- 6 Homotopy Pushouts and Pullbacks -- 7 Homotopy and Homology Decompositions -- 8 Homotopy Sets -- 9 Obstruction Theory -- A Point-Set Topology -- B The Fundamental Group -- C Homology and Cohomology -- D Homotopy Groups and the n-Sphere -- E Homotopy Pushouts and Pullbacks -- F Categories and Functors -- Hints to Some of the Exercises -- References -- Index.-.
520 _aThis is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: • Basic homotopy; • H-spaces and co-H-spaces; • Fibrations and cofibrations; • Exact sequences of homotopy sets, actions, and coactions; • Homotopy pushouts and pullbacks; • Classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; • Homotopy sets; • Homotopy and homology decompositions of spaces and maps; and • Obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. This approach provides a unifying motif, clarifies many concepts, and reduces the amount of repetitious material. The subject matter is treated carefully with attention to detail, motivation is given for many results, there are several illustrations, and there are a large number of exercises of varying degrees of difficulty. It is assumed that the reader has had some exposure to the rudiments of homology theory and fundamental group theory; these topics are discussed in the appendices. The book can be used as a text for the second semester of an algebraic topology course. The intended audience of this book is advanced undergraduate or graduate students. The book could also be used by anyone with a little background in topology who wishes to learn some homotopy theory.
650 0 _aMathematics.
650 0 _aAlgebraic topology.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Topology.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441973283
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-7329-0
912 _aZDB-2-SMA
999 _c105737
_d105737