Cameron Gordon
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View article: Characters in Low-Dimensional Topology
Characters in Low-Dimensional Topology Open
We study SL2(F)-character varieties of knots over algebraically closed fields F. We give a sufficient condition in terms of the double branched cover of a 2-bridge knot (or, equivalently, of its Alexander polynomial) on the characteristic …
View article: Higher-dimensional knot groups and decision problems
Higher-dimensional knot groups and decision problems Open
An $n$-knot is a locally flat PL $n$-sphere in $S^{n+2}$. We show that many decision problems about $n$-knot groups, $n \ge 3$, and groups of closed orientable surfaces in $S^4$, are unsolvable. We will also discuss the case of 2-knots, wh…
View article: ADE links and cyclic branched covers
ADE links and cyclic branched covers Open
The Dynkin diagrams of types A,D and E arise in many classification problems in mathematics. We conjecture a modest addition to this list: the fibered links that induce the standard tight contact structure on $S^3$ and have some cyclic bra…
View article: Knot contact homology detects cabled, composite, and torus knots
Knot contact homology detects cabled, composite, and torus knots Open
Knot contact homology is an invariant of knots derived from Legendrian contact homology which has numerous connections to the knot group. We use basic properties of knot groups to prove that knot contact homology detects every torus knot. …
View article: Bridge number and integral Dehn surgery
Bridge number and integral Dehn surgery Open
In a 3-manifold M, let K be a knot and R be an annulus which meets K\ntransversely. We define the notion of the pair (R,K) being caught by a surface\nQ in the exterior of the link given by K and the boundary curves of R. For a\ncaught pair…