Exponential growth and an asymptotic formula for the ranks of homotopy groups of a finite 1-connected complex - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annals of Mathematics Année : 2009

Exponential growth and an asymptotic formula for the ranks of homotopy groups of a finite 1-connected complex

(1) , (2) , (3)
1
2
3

Résumé

Let X be an n-dimensional, finite, simply connected CW complex and set αX = lim supi (log rank πi (X))/i. We prove that either rank πi (X) = 0 , i > 2n , or else that 0 < αX < ∞ and that for any ε > 0 there is a K = K(ε) such that k+n e(αX-ε)k ≤ k+nΣ rank πi (X) e(αx+ε)k, for all k ≥ K. i=k+2 In particular, this sum grows exponentially in k.

Dates et versions

hal-03031599 , version 1 (30-11-2020)

Identifiants

Citer

Yves Felix, Steve Halperin, Jean-Claude Thomas. Exponential growth and an asymptotic formula for the ranks of homotopy groups of a finite 1-connected complex. Annals of Mathematics, 2009, 170 (1), pp.443 - 464. ⟨10.4007/annals.2009.170.443⟩. ⟨hal-03031599⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook Twitter LinkedIn More