[FOM] Candidates for Harvey Friedman's Pi^0_1 formula P(n)
JoeShipman at aol.com
Thu Mar 18 13:27:54 EST 2004
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.
-- Joe Shipman
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