𝜋_{*}-kernels of Lie groups

Maruyama, Ken-ichi

doi:10.1090/S0002-9947-06-04199-7

$\boldsymbol {\pi _*}$-kernels of Lie groups
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by Ken-ichi Maruyama PDF

Trans. Amer. Math. Soc. 358 (2006), 2335-2351 Request permission

Abstract:

We study a filtration on the group of homotopy classes of self maps of a compact Lie group associated with homotopy groups. We determine these filtrations of $SU(3)$ and $Sp(2)$ completely. We introduce two natural invariants $lz_p(X)$ and $sz_p(X)$ defined by the filtration, where $p$ is a prime number, and compute the invariants for simple Lie groups in the cases where Lie groups are $p$-regular or quasi $p$-regular. We apply our results to the groups of self homotopy equivalences.

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