The Connective K-theory of Spinor Groups
نویسنده
چکیده
In a previous paper [4] we obtained the Hopf algebra structure of k*(G ; Q(P» where G is a compact connectvd Lie group and Q(P) is the quotient ring of Z with respect to a multiplicative subset generated by a set of primes, such that H*(G ; Q(P)) is torsion free . Here we study the properties of the connective K-theory of the Lie groups Spin(n) . Since H*(Spin(n) ; Z) is torsion free if n _< 6, we are only interested in the cases where n >_ 7. We will see that k*(Spin(n)) has only two torsion and we will give the algebra structure of k*(Spin(n) ; Z2)l{x E k*(Spin(n) ; Z 2 ) t-'x = 0} for n > 7 (t-1 is the canonical generator of k*(pt)). Our paper generalises part of earlier work of L . Hodgkin, who computed the usual K-theory of compact Lie groups [3] .
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