Editing Talk:Exotic sphere (section)

== What value of k in Brieskorn's complex manifold equation (the intersection of that manifold and a "small" (10-)sphere around the origin) yeilds a "non-exotic" homotopy 7-sphere? ==

"As shown by {{harvs|txt=yes|first=Egbert |last=Brieskorn|year=1966|year2=1966b}} (see also {{harv|Hirzebruch|Mayer|1968}}) the intersection of the [[complex manifold]] of points in '''C'''<sup>5</sup> satisfying
:<math>a^2 + b^2 + c^2 + d^3 + e^{6k-1} = 0\ </math>
with a small sphere around the origin for ''k'' = 1, 2, ..., 28 gives all 28 possible smooth structures on the oriented 7-sphere."
First of all, does the radius of the sphere matter?  If not, the word 'small' should probably be removed.  But my main question is, which of the 28 possible values of ''k'' in the equation for the non-spherical complex manifold results in a manifold whose intersection with a 10-sphere around the origin (presumably of any radius) yeilds a smooth structure on the oriented 7-sphere that ''is'' diffeomorphic to a 7-sphere?  [[User:Kevin Lamoreau|Kevin Lamoreau]] ([[User talk:Kevin Lamoreau|talk]]) 22:29, 16 October 2010 (UTC)
:(Corrected to replace "is not" with "''is''.") [[User:Kevin Lamoreau|Kevin Lamoreau]] ([[User talk:Kevin Lamoreau|talk]]) 19:33, 27 November 2010 (UTC)

: Didn't Brieskorn answer that question in his paper, cited in the main article?  [[User:Rybu|Rybu]] ([[User talk:Rybu|talk]]) 15:35, 11 April 2011 (UTC)

::Probably, but I couldn't find it in the first of the three links cited in that area of the article, and the other two are in German (which I don't speak) and are either only partially shown or largely restricted to subsribers. [[User:Kevin Lamoreau|Kevin Lamoreau]] ([[User talk:Kevin Lamoreau|talk]]) 20:35, 29 May 2011 (UTC)