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Introduction

In this chapter we introduce two universal constructions that successively kill homotopy groups of a space — the Postnikov tower (kills high-degree $\pi_*$) and the Whitehead tower (kills low-degree $\pi_*$) — and we apply the Whitehead tower together with the Serre spectral sequence to compute the second stable stem $\pi_2^s \cong \pi_5(S^3) \cong \mathbb{Z}/2\text{.}$

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