Constructing Lefschetz-type fibrations on four-manifolds
Copyright policy )Constructing Lefschetz-type fibrations on four-manifolds
We show how to construct broken, achiral Lefschetz fibrations on arbitrary smooth, closed, oriented 4-manifolds. These are generalizations of Lefschetz fibrations over the 2-sphere, where we allow Lefschetz singularities with the non-standard orientation as well as circles of singularities corresponding to round 1-handles. We can also arrange that a given surface of square 0 is a fiber. The construction is easier and more explicit in the case of doubles of 4-manifolds without 3- and 4-handles, such as the homotopy 4-spheres arising from nontrivial balanced presentations of the trivial group.
42 pages, 13 figures
- University of Cape Town South Africa
- University of California, Berkeley United States
Symplectic and contact topology in high or arbitrary dimension, 57M50 (Primary), 57R17 (Secondary), near-symplectic forms, Geometric Topology (math.GT), open book decompositions, round handles, 57M50, Mathematics - Geometric Topology, Andrews–Curtis conjecture, broken, Mathematics - Symplectic Geometry, open book decomposition, General geometric structures on low-dimensional manifolds, FOS: Mathematics, Gluck construction, achiral, Lefschetz fibrations, Symplectic Geometry (math.SG), achiral Lefschetz fibration, Surgery and handlebodies, 57R17
Symplectic and contact topology in high or arbitrary dimension, 57M50 (Primary), 57R17 (Secondary), near-symplectic forms, Geometric Topology (math.GT), open book decompositions, round handles, 57M50, Mathematics - Geometric Topology, Andrews–Curtis conjecture, broken, Mathematics - Symplectic Geometry, open book decomposition, General geometric structures on low-dimensional manifolds, FOS: Mathematics, Gluck construction, achiral, Lefschetz fibrations, Symplectic Geometry (math.SG), achiral Lefschetz fibration, Surgery and handlebodies, 57R17
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