Finite 2-group actions on the Chern manifold
by
Reinhard Schultz
Purdue University

Up to homeomorphism there is a unique 4-manifold that is homotopy equivalent but not homeomorphic to the complex projective plane; i.e., the Chern manifold. Results of Kwasik, Wilczynski and others during the nineteen eighties showed that this manifold admits a large assortment of odd order cyclic group actions. The main result of this work is that the Chern manifold admits no nontrivial involutions that induce the identity on homology; it follows that the cyclic group of order 2 is the only finite 2-group that can act effectively on this manifold. The proof uses a mixture of techniques from cohomological fixed point theory and controlled surgery theory; this is joint work with Slawomir Kwasik.

Date received: February 1, 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-57.