Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The main purpose of this thesis is to study the following question: Do primitives and sphericals agree in MU(,*)(X)/tor when X is a 1-connected compact Lie group. Our answers appear in Part IV for the classical groups (stable cases) and in Part V for two exceptional cases namely G(,2) and F(,4) (ignoring the prime 2).;The main tool for our study is the rational MU operation P : MU(,*)(X)(CRTIMES) (--->) MU(,*)(X)(CRTIMES) ; P = (SIGMA)(,E) m(,E)S(,E) which detects primitives rationally. Our method is to find the least positive integer k(,(alpha)) (ELEM) such that k(,(alpha))P((alpha)) (ELEM) MU(,*)(X)/tor (L-HOOK) MU(,*)(X)(CRTIMES) for (alpha) (ELEM) MU(,*)(X)/tor. This is done in Part III (SECTION)1. In Part III (SECTION)2 and (SECTION)3, we calculate the primitive elements in MU(,*)((//C)P('(INFIN))) and MU(,*)(HP('(INFIN))) respectively. In (SECTION)4 we establish a relation between P and ch*:K*(X) (--->) H**(X,Q) the Chern character, as well as between the integrality problem mentioned above and Chern character integrality condition.



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