geometry theory of Foliations

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1、CésarCamachoAlcidesLinsNetoGeometricTheoryofFoliationsTranslatedbySueE.GoodmanBIRKH.kUSERBoston•Basel•StuttgartLibraryofCongressCataloginginPublicationDataCamacho,Cesar,1943-Geometrictheoryoffoliations.Translationof:Teoriageometricadasfolheacoes.Bibliography:p.

2、Includesindex.1.Foliations(Mathematics)2.Geometry,Differential.I.LinsNeto,Alcides,1947-.II.Title.QA613.62.C36131985514'.7384-10978ISBN0-8176-3139-9CIP-KurztitelaufnahmederDeutsch,enBibliothekCamacho,César:Geometrictheoryoffoliations/CésarCamacho;AlcidesLinsNeto

3、.Transi.bySueE.Goodman-Boston;Basel;Stuttgart:Birichauser,1985.Einheitssacht.:TheoriageométricadasfolheagôesISBN3-7643-3139-9NE:LinsNeto,Alcides:27Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorby

4、anymeans,electronic,mechanical,photocopying,recordingorotherwise,withoutpriorpermissionofthecopyrightowner.©BirkhAuserBoston,Inc.,1985ISBN0-8176-3139-9ISBN3-7643-3139-9CONTENTSIntroduction1ChapterI—DifferentiableManifolds§1.Differentiablemanifolds5§2.Thederivat

5、ive13§3.Immersionsandsubmersions14§4.Submanifolds16§5.Regularvalues17§6.Transversality17§7.Partitionsofunity18ChapterII—Foliations§1.Foliations21§2.Theleaves31§3.Distinguishedmaps32§4.Planefieldsandfoliations35§5.Orientation36§6.Orientabledoublecoverings37§7.Or

6、ientableandtransverselyorientablefoliations38NotestoChapterII41ChapterIII—TheTopologyoftheLeaves§1.Thespaceofleaves47§2.Transverseuniformity48§3.Closedleaves51§4.Minimalsetsoffoliations52NotestoChapterIII53ChapterIV—HolonomyandtheStabilityTheorems§1.Holonomyofa

7、leaf62§2.Determinationofthegermofafoliationina67neighborhoodofaleafbythetheholonomyoftheleaf§3.Globaltrivializationlemma69§4.Thelocalstabilitytheorem70§5.Globalstabilitytheorem.Transverselyorientablecase72§6.Globalstabilitytheorem.Generalcase78NotestoChapterIV8

8、0ChapterV—FiberBundlesandFoliations§1.Fiberbundles87§2.Foliationstransversetothefibersofafiberbundle91§3.Theholonomyof5.93§4.Suspensionofarepresentation93§5.Existenceofgerms