Bott Periodicity Theorem

Define

			(1)
			(2)
			(3)

Then

			(4)
			(5)
			(6)

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More things to try:

.999 with 123 repeating
curl [-y/(x^2+y^2), -x/(x^2+y^2), z]
lim (f(x+h) - 2f(x) + f(x-h)) / h^2 as h->0

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.

Cite this as:

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