Henri Poincar&amp#233; Papers on Topology analysis situs and its five supplements 2010.pdf

《Henri Poincar&amp#233; Papers on Topology analysis situs and its five supplements 2010.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、PapersonTopologyAnalysisSitusandItsFiveSupplementsHenriPoincar¶eTranslatedbyJohnStillwellJuly31,20092ContentsTranslator'sIntroduction1TopologybeforePoincar¶e.........................1Poincar¶ebeforetopology..........................3TheAnalysissituspaper.........................5The¯vesupplements

2、............................7ThePoincar¶econjecture..........................9Commentsonterminologyandnotation.................11Acknowledgements.............................12Bibliography................................12OnAnalysisSitus15AnalysisSitus18Introduction...............................

3、..18x1.Firstde¯nitionofmanifold......................20x2.Homeomorphism............................22x3.Secondde¯nitionofmanifold.....................24x4.Oppositelyorientedmanifolds.....................28x5.Homologies...............................30x6.Bettinumbers.............................30

4、x7.Theuseofintegrals..........................32x8.Orientableandnon-orientablemanifolds...............34x9.Intersectionoftwomanifolds.....................40x10.Geometricrepresentation.......................49x11.Representationbyadiscontinuousgroup..............54x12.Thefundamentalgroup...........

5、............58x13.Fundamentalequivalences......................60x14.Conditionsforhomeomorphism...................65x15.Othermodesofgeneration......................75x16.ThetheoremofEuler.........................85x17.Thecasewherepisodd.......................93x18.Secondproof.....................

6、........9534ContentsSupplementtoAnalysisSitus100xI.Introduction...............................100xII.Schemaofapolyhedron........................103xIII.ReducedBettinumbers.......................107xIV.Subdivisionofpolyhedra.......................111xV.In°uenceofsubdivisiononreducedBettinumbers...

7、......112xVI.ReturntotheproofsofparagraphIII................117xVII.Reciprocalpolyhedra........................120xVIII.Proofofthefundamentaltheorem.................126xIX.Variousremarks............................130x