Invariants of totally real Lefschetz fibrations

Nermin Salepci

Vol. 256 (2012), No. 2, 407–433

DOI: 10.2140/pjm.2012.256.407

Abstract

We introduce certain invariants of real Lefschetz fibrations and call these invariants real Lefschetz chains. We prove that if the fiber genus is greater than 1, then the real Lefschetz chains are complete invariants of totally real Lefschetz fibrations. If however the fiber genus is 1, real Lefschetz chains are not sufficient to distinguish real Lefschetz fibrations. We show that by adding a certain binary decoration to real Lefschetz chains, we get a complete invariant.

Keywords

Lefschetz fibrations, real structure, monodromy

Mathematical Subject Classification 2010

Primary: 55R15, 55R55

Secondary: 57M05

Milestones

Received: 21 April 2011

Accepted: 14 December 2011

Published: 30 May 2012