Contact round surgery and Lutz twists

Abstract

From the viewpoint of contact round surgery, the Lutz twist and the Giroux torsion on contact [Formula: see text]-manifolds are studied in this paper. It is proved that the Lutz twist along a transverse knot and that along a pre-Lagrangian torus are realized by contact round surgeries of index [Formula: see text] and [Formula: see text] of contact [Formula: see text]-manifolds. This construction gives an important perspective on the Lutz twists. Both can be regarded as fiberwise connected sums with the compactified Lutz twist elements.