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ON VASSILIEV INVARIANTS FOR LINKS IN HANDLEBODIES
, 1997
"... Abstract. The notion of Vassiliev algebra in case of hanlebodies is developed. The analogues of the results of John Baez for links in handlebodies are proved. That means that there exists a onetoone correspondence between the special class of finite type invariants of links in hanlebodies and the ..."
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invariants introduced by V. A. Vassiliev [1] attracted a lot of attention and are studied deeply from various points of view as well as their connections with other fields of mathematics. In spite of the short period of time there exists a big amount of works on this subject.
GLUING TIGHT CONTACT STRUCTURES
, 2002
"... We prove gluing theorems for tight contact structures. As special cases, we rederive gluing theorems due to V. Colin and S. MakarLimanov and present an algorithm for determining whether a given contact structure on a handlebody is tight. As applications, we construct a tight contact structure on a ..."
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Cited by 227 (27 self)
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We prove gluing theorems for tight contact structures. As special cases, we rederive gluing theorems due to V. Colin and S. MakarLimanov and present an algorithm for determining whether a given contact structure on a handlebody is tight. As applications, we construct a tight contact structure on a
HANDLEBODYPRESERVING FINITE GROUP ACTIONS ON HAKEN MANIFOLDS WITH HEEGAARD GENUS TWO II
, 902
"... Abstract. Let M be a closed orientable 3manifold of Heegaard genus two with a nontrivial JSJdecomposition and G be a finite group of orientationpreserving diffeomorphisms acting on M which preserves each handlebody of Heegaard splitting and each piece of the JSJdecomposition of M. Let (V1, V2; ..."
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Cited by 1 (1 self)
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Abstract. Let M be a closed orientable 3manifold of Heegaard genus two with a nontrivial JSJdecomposition and G be a finite group of orientationpreserving diffeomorphisms acting on M which preserves each handlebody of Heegaard splitting and each piece of the JSJdecomposition of M. Let (V1, V2
On the geometric and algebraic rank of graph manifolds
, 2003
"... Abstract. For any n ∈ N we construct graph manifolds of genus 4n that have 3ngenerated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3manifold M is an embedded orientable surface S such that M − S consists of 2 handlebodies V1 and V2. This decomposition of M is call ..."
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Cited by 16 (1 self)
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Abstract. For any n ∈ N we construct graph manifolds of genus 4n that have 3ngenerated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3manifold M is an embedded orientable surface S such that M − S consists of 2 handlebodies V1 and V2. This decomposition of M
Let M be a closed orientable 3manifold of Heegaard genus two with a nontrivial
, 902
"... Abstract. Let M be a closed orientable 3manifold of Heegaard genus two with a nontrivial JSJdecomposition and G be a finite group of orientationpreserving smooth actions on M which preserves each handlebody of Heegaard splitting and each piece of the JSJdecomposition of M. Let (V1, V2; F) be th ..."
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Abstract. Let M be a closed orientable 3manifold of Heegaard genus two with a nontrivial JSJdecomposition and G be a finite group of orientationpreserving smooth actions on M which preserves each handlebody of Heegaard splitting and each piece of the JSJdecomposition of M. Let (V1, V2; F
DISTANCES OF HEEGAARD SPLITTINGS
, 2003
"... Abstract. J. Hempel in [6] showed that the set of distances of the Heegaard splittings (S, V, h n (V)) is unbounded, as long as the stable and unstable laminations of h avoid the closure of V ⊂ PML(S). Here h is a pseudoAnosov homeomorphism of a surface S while V is the set of isotopy classes of si ..."
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Cited by 7 (1 self)
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of simple closed curves in S bounding essential disks in a fixed handlebody. With the same hypothesis we show that the distance of the splitting (S, V, h n (V)) grows linearly with n, answering a question of A. Casson. In addition we prove the converse of Hempel’s theorem. Our method is to study the action
ARC DISTANCE EQUALS LEVEL NUMBER
, 901
"... Abstract. Let K be a knot in 1bridge position with respect to a genusg Heegaard surface that splits a 3manifold M into two handlebodies V and W. One can move K by isotopy keeping K ∩ V in V and K ∩ W in W so that K lies in a union of n parallel genusg surfaces tubed together by n −1 straight tube ..."
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Abstract. Let K be a knot in 1bridge position with respect to a genusg Heegaard surface that splits a 3manifold M into two handlebodies V and W. One can move K by isotopy keeping K ∩ V in V and K ∩ W in W so that K lies in a union of n parallel genusg surfaces tubed together by n −1 straight
A PRESENTATION FOR THE AUTOMORPHISMS OF THE 3SPHERE THAT PRESERVE A GENUS TWO HEEGAARD SPLITTING
, 2006
"... Abstract. Scharlemann constructed a connected simplicial 2complex Γ with an action by the group H2 of isotopy classes of orientation preserving homeomorphisms of S 3 that preserve the isotopy class of an unknotted genus 2 handlebody V. In this paper we prove that the 2complex Γ is contractible. Th ..."
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Abstract. Scharlemann constructed a connected simplicial 2complex Γ with an action by the group H2 of isotopy classes of orientation preserving homeomorphisms of S 3 that preserve the isotopy class of an unknotted genus 2 handlebody V. In this paper we prove that the 2complex Γ is contractible
Hiroshima Math. J. 30 (2000), 415±435 On nonsingular stable maps of 3manifolds with boundary into the plane
, 1999
"... ABSTRACT. Let M be a compact connected orientable 3manifold with nonempty boundary and f: M! R2 a stable map. In this paper we study the existence of an immersion or embedding lift of f to Rn
nV 3 with respect to the standard projection Rn! R2. We also characterize the orientable 3dimensional h ..."
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handlebody in terms of stable maps which have only a restricted class of singularities. Moreover, by using the concept of an embedding lift of a certain map of a 2dimensional polyhedron into R2, we give a characterization of S3. 1.
WILD ARCS IN THREESPACE 2: AN INVARIANT OF NONORIENTED LOCAL TYPE
, 1973
"... An invariant of the oriented local type of a FoxArtin arc has already been developed in the previous paper in this sequence. This paper is concerned with finding: an invariant of the nonoriented local type of an arc whose only wild point is an endpoint, where the arc has penetration index at least ..."
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work with 3cells as in [6], our cutting and pasting arguments will be applied to sequences of solid tori, making use of the theorems of H. Schubert ([7], §§16, 17). The notations Bd, Cl, Int, N(X), v{k Π X) are used as in [6]. 1. & is an oriented arc in Euclidean 3space R3 (the orientation of R3
Results 1  10
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12