Anick's conjecture for spaces with decomposable Postnikov invariants
(2004) Cambridge Philosophical Society. Mathematical Proceedings — Vol. 137, p. 559-570 (2004)
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- Abstract
- An elliptic space is one whose rational homotopy and rational cohomology are both finite dimensional. David Anick conjectured that any simply connected finite CW-complex S can be realized as the k-skeleton of some elliptic complex as long as k > dim S, or, equivalently, that any simply connected finite Postinkov piece S can be realized as the base of a fibration F-->E-->S where E is elliptic and F is k-connected, as long as the k is larger than the dimension of any homotopy class of S. This conjecture is only known in a few eases, and here we show that in particular if the Postnikov invariants of S are decomposable, then the Anick conjecture holds for S. We also relate this conjecture with other finiteness properties of rational spaces.
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Félix, Y., Jessup, B., & Murillo-Mas, A. (2004). Anick’s conjecture for spaces with decomposable Postnikov invariants. Cambridge Philosophical Society. Mathematical Proceedings, 137, 559-570. https://doi.org/10.1017/S0305004104007777 (Original work published 2004)