Félix, Yves
[UCL]
Jessup, B
Murillo-Mas, A
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.
Bibliographic reference |
Félix, Yves ; Jessup, B ; Murillo-Mas, A. Anick's conjecture for spaces with decomposable Postnikov invariants. In: Cambridge Philosophical Society. Mathematical Proceedings, Vol. 137, p. 559-570 (2004) |
Permanent URL |
http://hdl.handle.net/2078.1/39664 |