2001/10/04 by Jim Conant
Mathematics · #math.GT #msc:57M25 #msc:57M27
published as J. Knot Theory Ramifications, Vol. 12, No. 1 (2003) 47-52
arxiv created 2001/10/04 · arxiv updated 2009/11/30
In this paper, the easier methods of my thesis are applied to give a simple proof of a theorem of Goussarov. The theorem relates two possible notions of finite type equivalence of knots, links or string links, showing that the resulting filtrations are the same up to a degree shift by a factor of two. This is then applied to the situation of rooted claspers to show that rooted claspers of sufficiently high degree must preserve type k invariants. As a consequence, grope cobordisms of sufficiently high class must preserve type k invariants. This result is applied in math.GT/0012118, to show Theorem 2 of that paper.