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128
On the Kontsevich integral of Brunnian links
, 2006
"... The purpose of the paper is twofold. First, we give a short proof using the Kontsevich integral for the fact that the restriction of an invariant of degree 2n to (n+1)– component Brunnian links can be expressed as a quadratic form on the Milnor ¯µ linkhomotopy invariants of length n + 1. Second, we ..."
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Cited by 2 (2 self)
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The purpose of the paper is twofold. First, we give a short proof using the Kontsevich integral for the fact that the restriction of an invariant of degree 2n to (n+1)– component Brunnian links can be expressed as a quadratic form on the Milnor ¯µ linkhomotopy invariants of length n + 1. Second
SEIFERT MATRICES OF BRUNNIAN LINKS
, 2006
"... Abstract. We show some properties of a Seifert matrix of an ncomponent Brunnian link. In particular, we give a necessary and sufficient condition for a matrix to be a Seifert matrix of a 2component Brunnian link up to Sequivalence. ..."
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Abstract. We show some properties of a Seifert matrix of an ncomponent Brunnian link. In particular, we give a necessary and sufficient condition for a matrix to be a Seifert matrix of a 2component Brunnian link up to Sequivalence.
ON HOMOTOPY BRUNNIAN LINKS AND THE κINVARIANT
"... Abstract. We provide an alternative proof that Koschorke’s κinvariant is injective on the set of link homotopy classes of ncomponent homotopy Brunnian links BLM(n). The existing proof (by Koschorke [22]) is based on the Pontryagin–Thom theory of framed cobordisms, whereas ours is closer in spirit ..."
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Abstract. We provide an alternative proof that Koschorke’s κinvariant is injective on the set of link homotopy classes of ncomponent homotopy Brunnian links BLM(n). The existing proof (by Koschorke [22]) is based on the Pontryagin–Thom theory of framed cobordisms, whereas ours is closer in spirit
ON BRUNNIANTYPE LINKS AND THE LINK INVARIANTS GIVEN BY HOMOTOPY GROUPS OF SPHERES
, 2009
"... We introduce the (general) homotopy groups of spheres as link invariants for Brunniantype links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy groups measure the difference between the intersection subg ..."
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We introduce the (general) homotopy groups of spheres as link invariants for Brunniantype links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy groups measure the difference between the intersection
On surgery along Brunnian links in 3–manifolds
, 2006
"... We consider surgery moves along (n + 1)–component Brunnian links in compact connected oriented 3–manifolds, where the framing of the components is in { 1 k; k ∈ Z}. We show that no finite type invariant of degree < 2n − 2 can detect such a surgery move. The case of two linkhomotopic Brunnian lin ..."
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Cited by 4 (2 self)
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links is also considered. We relate finite type invariants of integral homology spheres obtained by such operations to Goussarov–Vassiliev invariants of Brunnian links.
Finite type invariants and Milnor invariants for Brunnian links
, 2006
"... A link L in the 3sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, the first author proved that the restriction to Brunnian links of any GoussarovVassiliev finite type invariant of (n + 1)component links of degree < 2n is trivial. The purpose of this pape ..."
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Cited by 6 (3 self)
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A link L in the 3sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, the first author proved that the restriction to Brunnian links of any GoussarovVassiliev finite type invariant of (n + 1)component links of degree < 2n is trivial. The purpose
ON SURGERY ALONG BRUNNIAN LINKS IN 3MANIFOLDS
, 2006
"... Abstract. We consider surgery moves along (n + 1)component Brunnian links in compact connected oriented 3manifolds, where the framing of the components is in { 1; k ∈ Z}. We show that no finite type invariant of degree k < 2n − 2 can detect such a surgery move. The case of two linkhomotopic Br ..."
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homotopic Brunnian links is also considered. We relate finite type invariants of integral homology spheres obtained by such operations to GoussarovVassiliev invariants of Brunnian links. 1.
ON SURGERY ALONG BRUNNIAN LINKS IN 3MANIFOLDS
, 2006
"... Abstract. We consider surgery moves along (n + 1)component Brunnian links in compact connected oriented 3manifolds, where the framing of the components is in { 1; k ∈ Z}. We show that no finite type invariant of dek gree 2n − 2 can detect such a surgery move. The case of two linkhomotopic Brunni ..."
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homotopic Brunnian links is also considered. We relate finite type invariants of integral homology spheres obtained by such operations to GoussarovVassiliev invariants of Brunnian links. 1.
Brunnian subgroups of mapping class groups and braid groups
, 2010
"... In this paper we continue our study of the Deltagroup structure on the braid groups and mapping class groups of a surface. We calculate the homotopy groups of these Deltagroups and prove some results about Brunnian braid groups and Brunnian mapping class groups. This is the second of a pair of pap ..."
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In this paper we continue our study of the Deltagroup structure on the braid groups and mapping class groups of a surface. We calculate the homotopy groups of these Deltagroups and prove some results about Brunnian braid groups and Brunnian mapping class groups. This is the second of a pair
BRUNNIAN LOCAL MOVES OF KNOTS AND VASSILIEV INVARIANTS
, 2004
"... K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of Ckmove. In this paper we give another geometric condition in terms of Brunnian local move. The proof is simple and selfcontained. 1. ..."
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K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of Ckmove. In this paper we give another geometric condition in terms of Brunnian local move. The proof is simple and selfcontained. 1.
Results 1  10
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128