Spun normal surfaces are a useful way of representing proper essential surfaces using ideal triangulations
for
–manifolds
with tori and Klein bottle boundaries. Walsh (2011) established that
proper essential surfaces which are not virtual fibers can be put into spun
normal form, so long as the triangulations have no edges isotopic into the
boundary. We use a different approach to study spun normal surfaces in
–efficient ideal
triangulations.
–efficiency
is a stronger condition than Walsh used, but we are able to deal with semifiber
surfaces. Moreover, fiber surfaces are shown to spin normalize, so long as there is a
closed normal surface in the infinite cyclic covering dual to the fibering. In two
followup papers, spinning essential surfaces in general ideal triangulations
will be considered and in the case of a single boundary component of the
–manifold,
all the boundary slopes of proper essential surfaces will be shown to occur at
vertices of the projective solution space, answering a question of Dunfield and
Garoufalidis.
Keywords
3–manifolds, normal surfaces, ideal triangulation, spun
normal surfaces
