61 citations · 235 across the 22 of their papers we have counts for
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math.GT2005★ 31 cited
Topology of spaces of knots in dimension 3
Ryan Budney
This paper is a computation of the homotopy type of K, the space of long knots in R^3, the same space of knots studied by Vassiliev via singularity theory. Each component of K corr…
math.GT2005★ 10 cited
JSJ-decompositions of knot and link complements in the 3-sphere
Ryan Budney
This paper is a survey of some of the most elementary consequences of the JSJ-decomposition and geometrization for knot and link complements in the 3-sphere. Formulated in the lang…
math.GT2005
On the homology of the space of knots
Ryan Budney, Frederick Cohen
Consider the space of `long knots' in R^n, K_{n,1}. This is the space of knots as studied by V. Vassiliev. Based on previous work of the authors, it follows that the rational homol…