紐結(jié)多項式不變量與三維流形量子不變量.pdf

1、浙江大學(xué)博士學(xué)位論文紐結(jié)多項式不變量與三維流形量子不變量姓名：周治修申請學(xué)位級別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)拓撲學(xué)指導(dǎo)教師：干丹巖20030601浙江火學(xué)博一學(xué)位論義摘要AbstractThebodyofthisthesisiscomposedofthreechaptersChapter1ThetripmatrixesforlinksLZulli[24]firstconstructedamatrix(mod2)forcomputingtheKa

2、uffmanbracketpolynomialsofknors，whichiscalledtripmatrixWestudiedthetripmatrixesoflinkshereThemainresultisTheorem31【fthestateSisobtainedfromthestateA4Abytogglingthelabelsinpositionsiji2，，mLetTxbethematrixobtainedfromthetr

3、ipmatrixbytogglingtheentriesinthecorrespondingpositionsalongthediagonalofthesubmatrixintheupleftcornerofTThen#fL／a)=腫m—rank(Ts)chapter2NotesonpolynomialinvariantsofK(A，印andK妒l，P2，，P。)TKanenobustudiedthestructureofpolynom

4、ialinvariantsofK(口，b)andKpI，p2，，仇)，wherea，b；p1p2，，nareallnumbertanglesWestudiedtheproperliesofthepolynomialinvariantsofK口，B)andK(P1，P2，，R)，whereA，占；PI，P2，，只：aregeneraltanglesThemainresultsareProposition212Inunorieotcase=

5、，胛∈zProposition213InorientcaseK(A2n，B2n)isskeinequivalentto剛，B)for行∈ZProposition222Inanarientcase，if^十五2‘五。=0，五∈Z，(i=12，，胛)，then=Proposition223InorientcaseP(K(暑2‘，最2五，，只2A))=JP(足(日，最，￡))where丑1丑2五。=0，丑∈Z，O=12，，”)，Theorem

6、221ThestatementsonK似，聊herearestillvalidforasequenceofKm(一，B)(m∈Z)(seeFig6inchapter2)Chapter3ModularCategoryThischapterconsistsoffoursectionsThemostcontentsofthefirstthreesectionsaretakenfom[231Thesection4isdevotetoasimil

7、arinvariantof3manifoldsgivenbytheauthorThemainresultisTheorem42t(M^)=璺一‘。一1x”一^‘塒?！眗(M。。^)isatopologicalinvariantofML，where“isthenumberofcomponentsofL，bl(Mlo)isthefirstBettinumberof舶，cListhelinkconsistingofcparallelcopie