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Journal of Operator Theory

Volume 46, Issue 2, Fall 2001  pp. 337-353.

The K-groups of $C(M)\times_\theta\bbb Z_p$ for certain pairs $(M,\theta)$

Authors Yifeng Xue
Author institution: Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P.R. China

Summary:  Let $M$ be a connected, compact metric space with $\dim M\le 2p-1$ ($p\ge 2$ is a prime) and let $\theta$ be a homeomorphism of $M$ to itself with period~$p$. Suppose that $\dim M_\theta\le 2$, $H^2(M_\theta,\bbb Z)$ $\cong 0$ and that $\bigoplus\limits^{2p-1}_{j=0}H^j(M/\theta,\bbb Z)$ is finitely generated and torsion-free; $H^0(M_\theta,\bbb Z)$ is finitely generated. If $\theta$ is regular and $H^{2j+1}(M/\theta,\bbb Z)\cong 0$, $1\le j\le p-1$ or $\theta$ is strongly regular and $M_\theta$ is connected, then $$\eqalign{ {\rm K}_0(C(M)\times_\theta\bbb Z_p)& \cong {\rm K}^0(M/\theta)\oplus\bigoplus\limits^{p-2}_{j=0}H^0(M_\theta,\bbb Z)\cr {\rm K}_1(C(M)\times_\theta\bbb Z_p)& \cong {\rm K}^{-1}(M/\theta)\oplus\bigoplus\limits^{p-2}_{j=0}H^1 (M_\theta,\bbb Z). \cr} $$ The result leads us to compute some interesting examples when $M$ is a sphere or a torus.

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