Riley's Conjecture on SL(2,R) Representations of 2-Bridge Knots
We prove Riley's conjecture on the number of parabolic SL(2,R) representations of 2-bridge knot groups.
math.GT↗
arXiv subjects
C. McA. Gordon
Publications and source records attributed to C. McA. Gordon.
Unsolvable problems about higher-dimensional knots and related groups
We consider classes of fundamental groups of complements of various kinds of codimension 2 embeddings and show that, in general, the problem of deciding whether or not a group in one class belongs to a smaller class is algorithmically unsolvable.
math.GR↗
On embedding infinite cyclic covers in compact 3-manifolds
We show that the infinite cyclic cover of the exterior of the untwisted Whitehead double of a non-trivial knot does not embed in any compact 3-manifold, answering a question of Jiang, Ni, Wang and Zhou.
math.GT↗
Toroidal and Boundary-Reducing Dehn Fillings
Let M be a simple 3-manifold with a toral boundary component partial_0 M. If Dehn filling M along partial_0 M one way produces a toroidal manifold and Dehn filling M along partial_0 M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on partial_0 M of the two filling slopes is at most two. In the special case that the boundary-reducing filling is actually a solid torus and the intersection number between the filling slopes is two, more is said to describe the toroidal filling.
math.GT↗