Journal of Lie Theory Volume 6 (1996) 19–22 C ◯1996 Heldermann Verlag

Complex Reflections

and Polynomial Generators of Homotopy Groups

Lucas M. Chaves and A. Rigas^{∗}

Communicated by K. Strambach

Abstract. Starting from suitable maps of the form ψ:𝕊^{n}→SU(m), for large m, we obtain functions θ:𝕊^{n}⟶SU(k) that generate π_{n} SU(k), for certain n and k. We have used this method in elementary algebraic topology courses for purposes of illustration, since it requires no machinery beyond the homotopy exact sequence of fibrations and provides an insight about the Bott periodicity theorems.

Universidade Federal de Lavras Cx. Postal 37 37.200-000 Lavras, MG, Brasil Instituto de Matemática Universidade Estadual de Campinas Cx. Postal 6065 13.081-970 Campinas, SP, Brasil

Received November 14, 1995

∗ Research partially supported by CNPq grant n^{o} 521067/94-4

ISSN 0949–5932 / $2.50 ^{_{C} ◯} Heldermann Verlag