In this paper we determine for relatively minimal elliptic surfaces with positive Euler number the image of the natural representation of the group of orientation preserving self-diffeomorphisms on \(\bar H\), the second homology group reduced modulo torsion. To this end we construct as many embedded spheres of square \(-2\) such that an isometry not induced from any combination of reflections at such spheres or from ‘complex conjugation’ can be shown not to be induced from some diffeomorphism at all. This is done with the help of Seiberg-Witten-invariants.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 18 December 1995 / Revised version: 27 January 1997
Rights and permissions
About this article
Cite this article
Lönne, M. On the diffeomorphism groups of elliptic surfaces. Math Ann 310, 103–117 (1998). https://doi.org/10.1007/s002080050139
Issue Date:
DOI: https://doi.org/10.1007/s002080050139