Mathematical Research Letters

Volume 5, Issue 2, March 1998 pp. 227-234.

Signatures, monopoles and mapping class groups

Authors: D. Kotschick
Author institution: Mathematisches Institut der Universität München

Summary: 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.

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