Mathematical Research Letters

Volume 5 (1998)

Number 2

Signatures, monopoles and mapping class groups

Pages: 227 – 234



D. Kotschick (Mathematisches Institut der Universität München)


Using the Seiberg–Witten monopole invariants of $4$–manifolds, we prove bounds on the signatures of surface bundles over surfaces. From these bounds we derive consequences concerning characteristic classes of flat bundles and the minimal genus of surfaces representing $2$–homology classes of mapping class groups.

Published 1 January 1998