Mathematical Research Letters
Volume 5 (1998)
Signatures, monopoles and mapping class groups
Pages: 227 – 234
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.