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Jul 2, 2012 at 18:41 comment added Jonathan Beardsley That's sort of what I thought might happen, you necessarily get really massive cell complexes or something. Geometric constructions of such things would be really interesting to see (in low dimensions at least).
Jul 2, 2012 at 4:56 comment added Sean Tilson I think Kathryn Hess discusses how you might think of the rationalized sphere in her notes on rational homotopy theory. As is alluded to below, i don't know that it is helpful geometrically. (she presents it as a cell complex, but it is huge)
Jul 1, 2012 at 3:54 vote accept Jonathan Beardsley
Jun 30, 2012 at 23:05 answer added cdouglas timeline score: 17
Jun 30, 2012 at 22:21 answer added Konrad Voelkel timeline score: 6
Jun 30, 2012 at 21:01 comment added Vidit Nanda I like the spirit of this question: visual intuition is often crucial in topology and geometry, and I would certainly benefit from good answers. However, I think it could be much improved if you focus on a question of the type: "are there good visual interpretations of homotopy theoretic constructions such as (blah), for instance by attaching cells?" rather than ask people whether they would personally find such constructions useful.
Jun 30, 2012 at 20:30 history asked Jonathan Beardsley CC BY-SA 3.0