Timeline for Examples of sphere bundles

8 events

when toggle format	what		by	license	comment
Dec 13, 2012 at 11:58	vote	accept	Dave
Dec 10, 2012 at 20:03	answer	added	Ryan Budney		timeline score: 5
Dec 10, 2012 at 19:59	comment	added	Dave		@Agol : Thank you for the link. Any references related to this question are much appreciated.
Dec 10, 2012 at 19:50	comment	added	Ian Agol		Hatcher has some notes (though no explicit example) - check out p. 8:math.cornell.edu/~hatcher/Papers/Diff(M)2012.pdf
Dec 10, 2012 at 19:30	comment	added	Dave		I would like to mention that I have posed this question on Stack Exchange a few days ago. Since no one has posted an actual example it was suggested to me that I should ask here on MathOverflow.
Dec 10, 2012 at 18:41	comment	added	Eric Peterson		If I may drag stable homotopy into it: the map assigning a stable spherical bundle to a stable vector bundle can be realized as a map $BO \to BGL_1 S$. Then, $BGL_1 S \simeq \Omega^\infty \Sigma^\infty S^0$, so in principle it should be easy to name a few such bundles: pick any element of $\pi_*^S$ which is guaranteed, for reasons of order, not to be in the image of this first map (since $\pi_m BO$ contains $2$-torsion at most). However, writing down geometric presentations of such bundles may be hard, and as these are stable statements, they will at best translate unstably only in a range...
Dec 10, 2012 at 18:12	history	edited	Dave	CC BY-SA 3.0	deleted 2 characters in body
Dec 10, 2012 at 18:04	history	asked	Dave	CC BY-SA 3.0