Toda譜Ⅴ（1）和Ⅴ（2）同倫群的一些新元素.pdf

1、南開大學碩士學位論文Toda譜Ⅴ（1）和Ⅴ（2）同倫群的一些新元素姓名：白建俠申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：林金坤20080401AbstractTodeterminethestablehomotopygroupsofsphere丌。SisthecentralanddifficultproblemsinhomotopytheoryinalgebraictopologyLetAbethemodPSteenrodalgebraa

2、ndSthespherespectrumlocalizedatanoddprimePLetA。bethedualityofAandPbethesubal—gebraofAgeneratedbyreducedpowersP(i≥0)WehavetheclassicalAdamsspectralsequence(ASS)：霹#=E耐岔(乙，乙)號磯一8S，whereE；ttermisthecohomologyofAThemostsucces

3、sfulmethodofcomputingtheExtgroupsistheMayspectralsequence(MSS)[9]：ForP2，thereexits曰^。兮E疵警(名，乙)suchthat日產(chǎn)一=E(hi，Ji0，歹≥0)oP(bi，ji0，J≥0)圓P(aili≥o)，whereEistheexterioralgebra，Pisthepolynomialalgebra，andht，J∈研’2∽一1)礦’2，bi，J∈E

4、22(pi1)p／lp(2i1)，ot∈磚2p‘一1，2州Inchapterone，bYusingAdamsspectr6tLsequence，itprovesthat(ili)。(6iko)and(ili)。(bko)arebothpermanentcirlesbutnotedges，andconvergetoannontrivialelementsof7ry(1)WherePisoddprimenumberq=2p一2Inchapt

5、ertwo，itprovesthat(i2ili)$(bill)convergestoannontrivialelementof丌。y(2)Theninchapterthree，wedeterminesometrivialornon—trivialresultsofExtgroupsbyusingtheMayspectralsequence(MSS)Keywords：Adamsspectral—sequence，Todaspectrum