gtm010 A Course in Simple Homotopy Theory

gtm010 A Course in Simple Homotopy Theory - M. M¡ Cohen...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: M. M¡ Cohen ,'\ A t ourse in Simple-HOmOtOpy TheOry / ' , Springer-VErlag N¡w YoRk· H¡Id¡lbeRG¢ B¡Rli£ Marshall M. Cohen AStE POf¡¢OR Of m£tH¤£tic, C O¥ e l L University, Ithaca AMS Subject Classif¡aTion (1970) 57 C 10 Al R¡gHtS RESERVEd. No p¢Rt of tH£S book m¢Y bE tR¢¤SlatEd oR REPRodu¥Ed £n anY foRm w£tHout wR£ttE¤ PERm£SS£o¤ fRom ¦PR£nGER-§ERL¢g¨ © 1 973 bY ¦pR£ngER-§ERªag NEW «oRk ¬n­® ¯£bR¢RY of CongRESS C¢taLo° C¢Rd NumbER 72-93439. ±R£¤tEd £¤ T ²n£tEd ¦t¢tES of ³mER£c¢´ -I ISBN 0-387-90055¡1 Springer VErlag ¡Ew York HEid ¢ lbErg £Erl¤n (soft covEr) ¥SB¦ 0¡387-90056¡X SprinGr-VErlag NEw York HEidElbErg BErl§n (hard covER) ISBN ¢£540-90055-1 Spr§ng¨r©VErlag ªErlin HEidEl«rg ¡EW YorK (soft covER) Ii I, I ¦ 1 I To Avis I S PREFACE This book grew out of courses which I taught at CoRelL Univers¡ty and ¢He £NiVers¡ty of Warwick duriNg 1969 aNd ¡970. I ¤rote it beca¥se of a s¢ro¦G BeLief ¢hA¢ ¢here sho§LD Be reADi¨Y A©Ai¨ABªe A semi-His¢orica¨ AND Geo« Me¢ri¬aLLY mo¢iVA¢eD exposi¢ioN of J. H. C¡ Whi¢e­eAD's BeA§¢¡f§L ¢HeorY oF simPLe-homo¢opy ¢Ypes; tha¢ the bes¢ ¤aY ¢o ¥¦ders¢aND ¢his ¢heory is to kno¤ how and why it was buil¢. This beLief is but¢ressed by the fact that the major uses of, and adVances iN, ¢he ¢heorY in receN¢ ¢imes®for examPLe, the S-cobor¯ism theorem (¯¡scussed iN §25), the use of ¢he theory in surgery, ¡¢s exteNsion to non-comPact compLexes (discussed a¢ ¢he enD of §6¢ and ¢he Proof of to°oLog¡caL invariance (GiveN in the ±PPendix)®have come from j²s¢ s³ch a´ understaNDinG. ± secoNd reason for ¤ri¢iNG ¢he book is peDagoGicaL. This is aN exceLLen¢ sµbject for a toPoLogy s¢udent to "Grow uP¶ on· The ¸nterpLay be¢¤een Geometry and aLgebra in ¢opoLoGY, eAc¹ eNricºinG the o¢her, ¡s bea¥¢if¥LLY ¡lLustrated in s¡mPLe»homotoPy theorY. The s¥bject ¡s accessibLe (as in the co¥rses mentioned at the o¥tset) to st¥dents who haVe had a good one¼ seMester course ¡n aLgebraic topoLogY½ I haVe tried to ¤ri¢e proofs ¤hich ¾eet the needs of ¿uch students· (Àhen a proof ¤as oÁitteD and Le as an exerc¡se, i¢ was Done ¤ith the ¤eLfare of the s¢udent in minD. Ãe sÄo¥Ld do s¥ch exercises zeaLo¥sÅy.) There is some ne¤ ma¢er¡aL hereÆ®for examPLe, the comPLeteLy geo¾etric ¯eÇni¢¡oN of the W¹¡tehead grouP of a comPLex in §6£ the obserVat¡ons on thE co¥n¢iNG of s¡mpLe-homotoPY ¢YPes ¡N §¤4£ and the Direc¢ °roof of the eq¥ivaLence of È¡LnorÉs deÇnit¡on of tors¡on ¤i¢­ the cLass¡caÅ DeÇnit¡on, Given in §16¥ Ê¥¢ ¾y Debt ¢o preVio¥s ¤orks on the s¥bJec¢ ¡s very great· I refer to [Kerva¡reËÈa¥marYËde̹amÍ, [ÎiLnor 1] and aboVe aÅL [Ï. Ã. C....
View Full Document

This note was uploaded on 05/14/2011 for the course MATHEMATIC 999 taught by Professor Charlesfefferman during the Spring '11 term at Princeton.

Page1 / 126

gtm010 A Course in Simple Homotopy Theory - M. M¡ Cohen...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online