A real open book not fillable by a real Lefschetz fibration

Abstract

A real 3- or 4-manifold has by definition an orientation preserving smooth involution acting on it. We consider Lefschetz fibrations of 4-dimensional manifolds-with-boundary and open book decompositions on their boundary in the existence of a real structure. We prove that there is a real open book which cannot be filled by a real Lefschetz fibration, although it is filled by non-real Lefschetz fibrations.

6 pages, 1 figure

References in corpus (3)

• Compact Stein surfaces with boundary as branched covers of $\B^4$
• Real elements in the mapping class group of $T^2$
• Products of pairs of Dehn twists and maximal real Lefschetz fibrations