On the ranks of homotopy groups of a space. (English) Zbl 0691.55011
For a simply connected space X of finite type and a prime p, let \(R_{\pi}\) and \(R_ H\) indicate the radii of convergence of the two power series \(P_{\pi}(X)=\sum (\dim \pi_ n(X)\otimes Z_ p)\cdot t^ n\) and \(P_ H(X)=\sum (\dim H_ n(\Omega X;Z_ p))\cdot t^ n,\) respectively. The author gives a partial answer to the Henn conjecture [H.-W. Henn, Manuscr. Math. 56, 235-245 (1985; Zbl 0605.55009)]. Namely, \(\min \{1,R_{\pi}\}\leq R_ H\) for all simply connected spaces of finite type.
Reviewer: Y.Furukawa
Citations:
Zbl 0605.55009References:
[1] | Bott, R. and Samelson, H., On the Pontrjagin product in spaces of paths, Comm. Math. Helv. 27 (1953), 320-337. · Zbl 0052.19301 · doi:10.1007/BF02564566 |
[2] | Henn, H. -W., On the growth of homotopy groups, Manuscripta Math. 56 (1986), 235-245. · Zbl 0605.55009 · doi:10.1007/BF01172158 |
[3] | Serre, J. -P., Cohomologie modulo 2 des complexes d’Eilenberg-MacLane, Comm. Math. Helv. 27 (1953), 198-232. · Zbl 0052.19501 · doi:10.1007/BF02564562 |
[4] | Umeda, Y., A remark on a theorem of J. -P. Serre, Proc. of Japan Academy, 35 (1959), 563-566. · Zbl 0108.17702 · doi:10.3792/pja/1195524215 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.