Classification of Actions of Finite Abelian Groups on Noncompact 2-Manifolds
by
Hongyu Ding
Indiana University

Classification of group actions on 2-manifolds is a classical question arising from the Nielsen realization problem. On an oriented, closed (i.e. compact and without boundary) 2-manifold, actions of a finite abelian group can be classified by their fixed point data and free cobordism classes (Neilsen, Edmonds). The main difficulties for studying group actions on a noncompact 2-manifold is that it may have infinite genus or infinitely many branch points. We introduce the end data and the type of a cluster end to classify the actions on oriented, noncompact 2-manifolds.

Date received: January 31, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-35.