03316nam 2200601 450 99646651960331620220907134148.03-540-39249-110.1007/BFb0079806(CKB)1000000000437482(SSID)ssj0000321693(PQKBManifestationID)12133494(PQKBTitleCode)TC0000321693(PQKBWorkID)10280362(PQKB)10185690(DE-He213)978-3-540-39249-1(MiAaPQ)EBC5584803(Au-PeEL)EBL5584803(OCoLC)1066182995(MiAaPQ)EBC6841872(Au-PeEL)EBL6841872(PPN)155237470(EXLCZ)99100000000043748220220907d1988 uy 0engurnn#008mamaatxtccrBoundedly controlled topology foundations of algebraic topology and simple homotopy theory /Douglas R. Anderson, Hans J. Munkholm1st ed. 1988.Berlin ;Heidelberg :Springer-Verlag,[1988]©19881 online resource (XIV, 310 p.)Lecture Notes in Mathematics ;Volume 1323Bibliographic Level Mode of Issuance: Monograph3-540-19397-9 Category 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.Several 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.Lecture notes in mathematics (Springer-Verlag) ;Volume 1323.Cobordism theoryCobordism theory.514.7257Q10mscAnderson Douglas R(Douglas Ross),1940-1255039Munkholm Hans J(Hans Jørgen),1940-MiAaPQMiAaPQMiAaPQBOOK996466519603316Boundedly controlled topology2909981UNISA