  We show that manifolds admitting special generic maps also admit nice
generalized multisections.
  Special generic maps are natural generalized versions of Morse functions with
exactly two singular points on closed manifolds, characterizing spheres whose
dimensions are not $4$ topologically and the $4$-dimensional unit sphere, and
canonical projections of unit spheres. They are shown to restrict the
differentiable structures of spheres etc. and topologies of more general
manifolds strongly by Saeki, Sakuma etc., followed by Nishioka, Wrazidlo etc.
and followed by the author. Some elementary or important manifolds also admit
such maps.
  (Generalized) multisections of manifolds are nice decompositions of (compact)
manifolds, generalizing so-called Heegaard splittings of $3$-dimensional
manifolds.
  PL manifolds have been shown to have (generalized) multisections enjoying
certain properties by Rubinstein and Tillmann.
