LEADER 03316nam 2200601 450 001 996466519603316 005 20220907134148.0 010 $a3-540-39249-1 024 7 $a10.1007/BFb0079806 035 $a(CKB)1000000000437482 035 $a(SSID)ssj0000321693 035 $a(PQKBManifestationID)12133494 035 $a(PQKBTitleCode)TC0000321693 035 $a(PQKBWorkID)10280362 035 $a(PQKB)10185690 035 $a(DE-He213)978-3-540-39249-1 035 $a(MiAaPQ)EBC5584803 035 $a(Au-PeEL)EBL5584803 035 $a(OCoLC)1066182995 035 $a(MiAaPQ)EBC6841872 035 $a(Au-PeEL)EBL6841872 035 $a(PPN)155237470 035 $a(EXLCZ)991000000000437482 100 $a20220907d1988 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBoundedly controlled topology $efoundations of algebraic topology and simple homotopy theory /$fDouglas R. Anderson, Hans J. Munkholm 205 $a1st ed. 1988. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1988] 210 4$d©1988 215 $a1 online resource (XIV, 310 p.) 225 1 $aLecture Notes in Mathematics ;$vVolume 1323 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-19397-9 327 $aCategory theoretic foundations -- The algebraic topology of boundedly controlled spaces -- The geometric, boundedly controlled whitehead group -- Free and projective rpg modules the algebraic whitehead groups of rpg -- The isomorphism between the geometric and algebraic whitehead groups -- Boundedly controlled manifolds and the s-cobordism theorem -- Toward computations. 330 $aSeveral recent investigations have focused attention on spaces and manifolds which are non-compact but where the problems studied have some kind of "control near infinity". This monograph introduces the category of spaces that are "boundedly controlled" over the (usually non-compact) metric space Z. It sets out to develop the algebraic and geometric tools needed to formulate and to prove boundedly controlled analogues of many of the standard results of algebraic topology and simple homotopy theory. One of the themes of the book is to show that in many cases the proof of a standard result can be easily adapted to prove the boundedly controlled analogue and to provide the details, often omitted in other treatments, of this adaptation. For this reason, the book does not require of the reader an extensive background. In the last chapter it is shown that special cases of the boundedly controlled Whitehead group are strongly related to lower K-theoretic groups, and the boundedly controlled theory is compared to Siebenmann's proper simple homotopy theory when Z = IR or IR2. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 1323. 606 $aCobordism theory 615 0$aCobordism theory. 676 $a514.72 686 $a57Q10$2msc 700 $aAnderson$b Douglas R$g(Douglas Ross),$f1940-$01255039 702 $aMunkholm$b Hans J$g(Hans Jørgen),$f1940- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466519603316 996 $aBoundedly controlled topology$92909981 997 $aUNISA