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Feb 14, 2011 at 18:24 comment added Sam Isaacson @Henrik, thanks for the correction. @Lennart, you're right; $p$-locally, the only delooping of $S^3$ is $\mathbf{H}\mathrm{P}^\infty$.
Feb 14, 2011 at 18:20 history edited Sam Isaacson CC BY-SA 2.5
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Feb 14, 2011 at 17:00 comment added Lennart Meier ad 1: it should be noted that this is really a global phenomenon. I think, at each prime the delooping is unique.
Feb 14, 2011 at 15:51 comment added Jeff Strom Regarding ghosts: for each $n$, there are maps $f$ of finite complexes such that $\Sigma ^{2k} f$ induces $0$ on $\pi_*$ for $2k\leq n$.
Feb 14, 2011 at 11:51 comment added Johannes Ebert Rectors example is really awesome. I cannot imagine uncountably many H-space structures on $S^3$.
Feb 14, 2011 at 10:23 comment added Johannes Ebert And these phantoms are then zero on homology, cohomology and homotopy.
Feb 14, 2011 at 9:52 comment added HenrikRüping i guess $if$ should be $fi$.
Feb 14, 2011 at 7:08 history answered Sam Isaacson CC BY-SA 2.5