Erratum to ``Topology of Hopf surfaces''
Masahide Kato · Journal of the Mathematical Society of Japan · 1989
The author was kindly informed by M. Ue that the statement of Theorem 9 was incomplete and a certain subcase was missing.As was pointed out by Ue, this error had its origin in Lemma 4 of the paper which claimed that $N_{SL(2.C)}(B_{n})=B_{2n}$ for $n\geqq 2$ .In fact, this equality holds for $n\geqq 3$ , but for $n=2$ , we have $N_{SL(2.C)}(B_{2})=D$ .By this mistake, we must correct Lemmas 4, 5, 6, 7, Proposition 8, and Theorem 9, though they hold true under the condition that $K eq B_{2}$ .The other results are OK without change.We correct these errors as follows.In Lemma 4, $N_{SL(2,C)}(B_{n})=B_{2n}(n\geqq 3),$ $N_{SL(2.C)}(B_{2})=D$ .In Lemma 5, $N_{GL(2.C)}(B_{n})=C^{*}I\cdot B_{2n}(n\geqq 3),$ $N_{GL(2,C)}(B_{2})=C^{*}I\cdot D$ .In Lemma 6, Case 2, for $K=B_{n}(n\geqq 3),$ $u=(\begin{array}{ll}\rho_{2n} 00 \rho_{2n}^{-1}\end{array})$ , and for $K=B_{2},$ $u=u_{1}$ $:=(\begin{array}{ll}\rho_{4} 00 p_{4}^{-1}\end{array})$ or $u=u_{2}$ $:=$ $\frac{1}{\sqrt{2}}(\begin{array}{ll}\rho_{4}^{3} \rho_{4}^{3}\rho_{4} -\rho_{4}\end{array})$ .In case $K=B_{2}$ , Lemma 7 should be replaced by