Homotopy Commutativity and Power Maps In Lie Groups Seminar

In the 1960’s and 1970’s, Arkowitz, McGibbon and others studied the homotopy commutativity of simply connected, compact, simple Lie groups and their p completions. McGibbon also gave a direct link between power maps and the exponent of the commutator subgroup of such Lie groups. Combining their collective results in theory gives a solution to the problem of determining the order of the commutator subgroup. However, their solution involves the calculation of a number N which is dependent on the Lie group. The value of this N is known in only a few small cases.

These results will be presented and then more recent work by Kaji, Kishimoto, Kono, Theriault, myself and others will be presented, and shown that these works help build and improve on the results of the 1960’s and 1970’s. If time allows I will then talk a little about what work is currently being done on this problem as well