Abigail Thompson

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It has been conjectured that the geometric invariant of knots in 3–space called the width is nearly additive. That is, letting w(K) ∈ 2N denote the width of a knot K ⊂ S 3 , the conjecture is that w(K#K ′) = w(K) + w(K ′) − 2. We give an example of a knot K 1 so that for K 2 any 2–bridge knot, it appears that w(K 1 #K 2) = w(K 1), contradicting the(More)
  • Geometry Topology, G G G G G G G G G G G G G G G, Hiroshi Goda, Martin Scharlemann, Abigail Thompson, Cameron Gordon +2 others
  • 2000
T T T T T T T T T T T T T T T Abstract It is a consequence of theorems of Gordon–Reid [4] and Thompson [8] that a tunnel number one knot, if put in thin position, will also be in bridge position. We show that in such a thin presentation, the tunnel can be made level so that it lies in a level sphere. This settles a question raised by Morimoto [6], who(More)
It has been postulated that autism spectrum disorder is underpinned by an 'atypical connectivity' involving higher-order association brain regions. To test this hypothesis in a large cohort of adults with autism spectrum disorder we compared the white matter networks of 61 adult males with autism spectrum disorder and 61 neurotypical controls, using two(More)
Let K be a knot with an unknotting tunnel γ and suppose that K is not a 2-bridge knot. There is an invariant ρ = p/q ∈ Q/2Z, p odd, defined for the pair (K, γ). The invariant ρ has interesting geometric properties: It is often straightforward to calculate; e. g. for K a torus knot and γ an annulus-spanning arc, ρ(K, γ) = 1. Although ρ is defined abstractly,(More)
It is shown, using sutured manifold theory, that if there are any 2-component counterexamples to the Generalized Property R Conjecture, then any knot of least genus among components of such counterexamples is not a fibered knot. The general question of what fibered knots might appear as a component of such a counterexample is further considered; much can be(More)
Suppose F is a compact orientable surface, K is a knot in F × I, and (F × I)surg is the 3-manifold obtained by some non-trivial surgery on K. If F × {0} compresses in (F × I)surg, then there is an annulus in F × I with one end K and the other end an essential simple closed curve in F × {0}. Moreover, the end of the annulus at K determines the surgery slope.(More)