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math.GT2005★ 3 cited
Roots of knotted graphs and orbifolds
Sergei Matveev
Let G be a graph in a 3-manifold M. We compress the pair (M,G) along admissible 2-spheres as long as possible. What we get is a root of (M,G). Our main result is that for any pair…
math.GT2005★ 2 cited
Roots of 3-manifolds and cobordisms
C. Hog-Angeloni, S. Matveev
Given a set of simplifying moves on 3-manifolds, we apply them to a given 3-manifold M as long as possible. What we get is a root of M. For us, it makes sense to consider three typ…
math.GT2002
Cubic complexes and finite type invariants
Sergei Matveev, Michael Polyak
Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite ty…