Keywords. Knotted surface, plane curve, mapping class group, spin mapping class group
AMS subject classification. Primary: 57Q45. Secondary: 57N05, 20F38.
Submitted: 13 February 2005. (Revised: 28 April 2005.) Accepted: 31 May 2005. Published: 30 June 2005.
Department of Mathematics, Faculty of Science and Engineering
Saga University, Saga, 840-8502 Japan.
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