000 03239nam a22004695i 4500
001 978-3-540-39249-1
003 DE-He213
005 20190213151509.0
007 cr nn 008mamaa
008 121227s1988 gw | s |||| 0|eng d
020 _a9783540392491
_9978-3-540-39249-1
024 7 _a10.1007/BFb0079806
_2doi
050 4 _aQA612-612.8
072 7 _aPBPD
_2bicssc
072 7 _aMAT038000
_2bisacsh
072 7 _aPBPD
_2thema
082 0 4 _a514.2
_223
100 1 _aAnderson, Douglas R.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aBoundedly Controlled Topology
_h[electronic resource] :
_bFoundations of Algebraic Topology and Simple Homotopy Theory /
_cby Douglas R. Anderson, Hans J. Munkholm.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1988.
300 _aXIV, 310 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1323
505 0 _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.
520 _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.
650 0 _aAlgebraic topology.
650 1 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
700 1 _aMunkholm, Hans J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662174098
776 0 8 _iPrinted edition:
_z9783540193975
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1323
856 4 0 _uhttps://doi.org/10.1007/BFb0079806
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10877
_d10877