[FOM] Candidates for Harvey Friedman's Pi^0_1 formula P(n)

[JoeShipman@aol.com]

Chow is mistaken.  Homotopy groups of spheres, indeed of any simply connected finite complexes, are computable (E.H. Brown, Jr, "Finite Computability of Postnikov Complexes", Annl. of Math. 65 (1957), 1-20).  The calculation is very complex, and for some reason topology textbooks don't seem to think this computability result interesting.

Although Brown's algorithm is impractical, Francis Sergeraert has developed a theory of "constructive algebraic topology" which has been implemented successfully on computers and solved many previously open problems about homotopy groups.

See: 
http://www-fourier.ujf-grenoble.fr/~sergerar/Papers/tenerife.ps

-- Joe Shipman