A number-theoretic approach to homotopy exponents of SU(n)

Donald M. Davis and Zhi-Wei Sun

dmd1@lehigh.edu
zwsun@nju.edu.cn

Lehigh University, Bethlehem, Pa, 18015
Nanjing University, Nanjing 210093, PRC

AMS Classifications: 55Q52, 57T20, 11A07, 11B65, 11S05

Abstract:
We use methods of combinatorial number theory to prove that,
for all n and p, some homotopy group pi_i(SU(n)) contains an
element of order p^{n-1+ord_p([n/p]!)}, where ord_p(m)
denotes the exponent of p in m.