高等数学

AnnalsofMathematics,157(2003),919–938

LargeRiemannianmanifolds

whichare exible

ByA.N.Dranishnikov,StevenC.Ferry,andShmuelWeinberger*

Abstract

Foreachk∈Z,weconstructauniformlycontractiblemetriconEuclideanspacewhichisnotmodkhypereuclidean.WealsoconstructapairofuniformlycontractibleRiemannianmetricsonRn,n≥11,sothattheresultingmani-foldsZandZ areboundedhomotopyequivalentbyahomotopyequivalencewhichisnotboundedlyclosetoahomeomorphism.Weshowthatfortheself(Z)→K (C (Z))fromlocally -spacestheC -algebraassemblymapK

niteK-homologytotheK-theoryoftheboundedpropagationalgebraisnotamonomorphism.ThisshowsthatanintegralversionofthecoarseNovikovcon-jecturefailsforrealoperatoralgebras.Ifweallowasinglecone-likesingularity,asimilarconstructionyieldsacounterexampleforcomplexC -algebras.

1.Introduction

Thispaperisacontributiontothecollectionofproblemsthatsurroundspositivescalarcurvature,topologicalrigidity(a.k.a.theBorelconjecture),theNovikov,andBaum-Connesconjectures.Muchworkinthisarea(seee.g.[14],

[4],[3],[15])hasfocusedattentiononboundedandcontrolledanaloguesoftheseproblems,whichanaloguesoftenimplytheoriginals.Recently,successinattacksontheNovikovandGromov-LawsonconjectureshasbeenachievedalongtheselinesbyprovingthecoarseBaum-Connesconjectureforcertainclassesofgroups[23],[27],[28].AformofthecoarseBaum-Connesconjec-lf(X)→K (C (X))isanturestatesthattheC -algebraassemblymapµ:K

isomorphismforuniformlycontractiblemetricspacesXwithboundedgeom-etry[21].

UsingworkofGromovonembeddingofexpandinggraphsingroupsΓwithBΓa nitecomplex[16],theepimorphismpartofthecoarseBaum-Connescon-

TheauthorsarepartiallysupportedbyNSFgrants.ThesecondauthorwouldliketothanktheUniversityofChicagoforitshospitalityduringnumerousvisits.

1991MathematicsSubjectClassi cation.53C23,53C20,57R65,57N60.

Keywordsandphrases.uniformlycontractible.

搜索“diyifanwen.net”或“第一范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读，第一范文网，提供最新高中教育高等数学全文阅读和word下载服务。