Year: 2010
Type: preprint
Abstract: Tollefson described a variant of normal surface theory for 3-manifolds, called Q-theory, where only the quadrilateral coordinates are used. Suppose $M$ is a triangulated, compact, irreducible, boundary-irreducible 3-manifold. In Q-theory, if $M$ contains an essential surface, then the projective solution space has an essential surface at a vertex. One interesting situation not covered by this theorem is when $M$ is boundary reducible, e.g. $M$ is an unknot complement. We prove that in this case $M$ has an essential disc at a vertex of the Q-projective solution space.
Source: arXiv (Cornell University)
Author: Suh, Chan-Ho
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1602277997