Homotopy nilpotency in localized $SU(n)$

Abstract

We determine the homotopy nilpotency of p-localized SU(n) when p is a quasi-regular prime in the sense of [9]. As a consequence, we see that it is not a monotonic decreasing function in p.

Homotopy nilpotency in p-regular loop spaces

“…As in the following theorem, one can expect that nilG ( p) is a monotonic decreasing function in p for a fixed Lie group G in most cases. But it is shown in [14] that this is false.…”

“…Remark 1 A continuation of Question 3 is considered by the second named author [14]. Actually, he considers the homotopy nilpotency of a p-localized SU(n) having the homotopy type of a product of spheres and sphere bundles over spheres.…”

“…Then, for (14) and (15), one has π(i * 2 (y 2 )) = π(i * 2 (y 8 )) = π(i * 2 (y 2 6 )) = π(i * 2 (y 14 y 10 )) = 0.…”

“…Sincez 2 ,z 8 ,z 12 are algebraically independent, we have: Let us consider the generator z 14 . For a dimensional reason, an element of degree 28 in F 37 [ p 1 , .…”

Commutativity of localized self-homotopy groups of symplectic groups

“…Then it is an interesting problem to consider for a fixed G, how the H-structure of G (p) changes when we vary p. Kaji and the first named author obtained a result for a Lie group G when p is relatively large [9,10]. Let us turn to the self-homotopy group H(G).…”