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On the ranks of homotopy groups of two-cones

✍ Scribed by Pascal Lambrechts

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
120 KB
Volume
108
Category
Article
ISSN
0166-8641

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✦ Synopsis

Let X be a finite simply-connected CW-complex of dimension n X . If X is a two-cone (that is: X is the homotopy cofiber of a map between suspensions) such that Ο€ * (X) βŠ— Q is infinite-dimensional, then there exist A, B > 0 and Ξ± > 1 such that for any positive integer k we have

This formula is proved by establishing some analytic property of the PoincarΓ© series Ω X (z) = ∞ n=0 dim H n (ΩX; Q) β€’ z n . These inequalities hold also for some other classes of spaces.

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