منابع مشابه
Markov Theorems for Links in 3-manifolds
We describe here a Markov theorem for links in S 2 S 1 using the braid groups corresponding to the Coxeter groups of type B l. See the theorem in x3. We will work on a more general setting. The only reason here to single out S 2 S 1 is its simplicity. It is possible that all the other Artin groups will turn out to be useful in the study of links in 3-manifolds.
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We introduce a complexity c(X) ∈ N for pairs X = (M, L), where M is a closed orientable 3-manifold and L ⊂ M is a link. The definition employs simple spines, but for well-behaved X's we show that c(X) equals the minimal number of tetrahedra in a triangulation of M containing L in its 1-skeleton. Slightly adapting Matveev's recent theory of roots for graphs, we carefully analyze the behaviour of...
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We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth cobordisms between two given closed 3-manifolds. As a consequence, there are finitely many smooth closed 4-manifolds constructed from some Kirby diagram with bou...
متن کاملUniversal Vassiliev invariants of links in coverings of 3-manifolds
We study Vassiliev invariants of links in a 3-manifold M by using chord diagrams labeled by elements of the fundamental group of M . We construct universal Vassiliev invariants of links in M , where M = P 2×[0, 1] is a cylinder over the real projective plane P 2, M = Σ× [0, 1] is a cylinder over a surface Σ with boundary, and M = S1 × S2. A finite covering p : N −→ M induces a map π1(p) ∗ betwe...
متن کاملAlgebraic Markov equivalence for links in 3-manifolds
Let Bn denote the classical braid group on n strands and let the mixed braid group Bm,n be the subgroup of Bm+n comprising braids for which the first m strands form the identity braid. Let Bm,∞ = ∪nBm,n. We will describe explicit algebraic moves on Bm,∞ such that equivalence classes under these moves classify links in a link complement or in a closed connected 3-manifold. The moves depend on a ...
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ژورنال
عنوان ژورنال: Topology
سال: 1971
ISSN: 0040-9383
DOI: 10.1016/0040-9383(71)90006-1