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Bott Periodicity Theorem

Define

O=lim_(->)O(n),F=R
(1)
U=lim_(->)U(n),F=C
(2)
Sp=lim_(->)Sp(n),F=H.
(3)

Then

Omega^2BU=BU×Z
(4)
Omega^4BO=BSp×Z
(5)
Omega^4BSp=BO×Z.
(6)

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References

Atiyah, M. F. K-Theory. New York: Benjamin, 1967.Bott, R. "The Stable Homotopy of the Classical Groups." Ann. Math. 70, 313-337, 1959.Dodson, C. T. J. and Parker, P. E. A User's Guide to Algebraic Topology. Dordrecht, Netherlands: Kluwer, p. 229, 1997.Milnor, J. W. Morse Theory. Princeton, NJ: Princeton University Press, 1963.

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Bott Periodicity Theorem

Cite this as:

Weisstein, Eric W. "Bott Periodicity Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BottPeriodicityTheorem.html

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