On Postnikov pieces of finite dimension

• Autores: Carles Casacuberta i Vergés
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 49, Fasc. 2-3, 1998, págs. 257-264
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We prove that, if $X$ is a connected CW-complex of finite dimension with only a finite number of nonzero Postnikov invariants, then the homotopy groups $\pi_n(X)$ are rational vector spaces for $n\geq 2$ and they vanish for all n sufficiently large. Moreover, the fundamental group $\pi_1(X)$ is torsion-free and all its abelian subgroups have finite rank. Our argument relies on Miller’s solution of a conjecture due to Sullivan.

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