三維流形上的把柄添加.pdf

1、大連理工大學(xué)博士學(xué)位論文三維流形上的把柄添加姓名：張明星申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：邱瑞鋒20070501大連理工大學(xué)博士學(xué)位論文HandleadditionsOil&manifoldsAbstractDehnsurgeryandHeegaardsplittingaretwoimportantmethodsofconstructing3manifoldsThesetwomethodsCallbeviewed船handlea

2、dditions缸animportantproblemofhandleadditions，itisinterestingtoconsiderthathowmany2handleadditionsonagenusatleasttwoboundarycomponentofahyperboSc3manifoldCanobtainanonhyperbolicmanifold，LetMbeahyperboficmanifold。andFbeaco

3、mponentofOMofgenusatleasttwoSupposeoand口aretwoseparatingslopsonFMScharlemannandYWuprovedthatif』l彳(a)and』I擴(kuò)(偽arenothyperbolic，thentheintersectionnumber△(o，∥)≤14Furthermore，theygaveaconjecture：ifM(口)andM(口)arereducibleorOr

4、educible，then△(Q，p)=0Inthispaper，weprovethatifbothM(a)andM(口)8xereducible，then△(Q，口)≤2SpeciallyifbothJ汀(口)andM03)arereducibleandthegenusofFis2，then△(Q，p)=0ThIsresulttogetherwiththeresultin【35】andtheresultin【56]indicatest

5、hatthereisoulyoneseparatingslopaonanycomponentFofOMofgenustwosuchthatMf01iseitherreducibleorOreducibleThismeansthattheaboveconjectureistruewhenthegenusofFistwo缸acorollaryoftheaboveresultswealsogiveapartialproofoftheRefil

6、lingconjecturewhichisgivenbyMScharlemannSuppose尬=Kum(i=1，2)areHeegaardsplittingsAhomeomorphism，：日_尼producesanattachedmanifoldM=％u五奶M2，where只C亂睨InthispaperwedefineasurfacesunlofHeegaardspfittingsinducedfromtheHeegaardspli

7、ttingsof尬andM2WealsogiveanexampleshowingthatthesurfacesumofHeegaardsp五ttingsisdifferentfromamalgamationofHeegaardsplittingsFurthermore，wegiveasufficientconditionwhenthesurfacesumofHeegaardsplittingsisstabilizedThinpositi

8、onofHeegaardsplittingsdefinedbyMScharlemannandAThompsonplaysanimportantroleinthestudyofHeegaardsplittings，UsingKneser—Haken’STheorem，weprovethatanynonexcessivesetofcompletelydNointbicompressiblesurfacescontainsonlyfinite