Motivated by M. Scharlemann and A. Thompson’s definition of thin
position of 3-manifolds, we define the width of a handle decomposition
a 4-manifold and introduce the notion of thin position of a compact
smooth 4-manifold. We determine all manifolds having width equal to
, and give a relation
between the width of
and its double
.
In particular, we describe how to obtain genus
and
trisection diagrams for sphere bundles over orientable and nonorientable surfaces of
genus
,
respectively. Finally, we study the problem of describing relative handlebodies as
cyclic covers of a 4-space branched along knotted surfaces from the width
perspective.
Keywords
Heegaard splittings, handle decompositions, thin position,
trisections of 4-manifolds, tunnel number of links
