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Results 1 - 10
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1,310
Heegaard splittings of graph manifolds
- Geometry & Topology
, 2004
"... Let M be a totally orientable graph manifold with characteristic submanifold T and let M = V ∪S W be a Heegaard splitting. We prove that S is standard. In particular, S can be isotoped so that for each vertex manifold N of M, S ∩ N is either horizontal, pseudohorizontal, vertical or pseudovertical. ..."
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Cited by 7 (1 self)
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Let M be a totally orientable graph manifold with characteristic submanifold T and let M = V ∪S W be a Heegaard splitting. We prove that S is standard. In particular, S can be isotoped so that for each vertex manifold N of M, S ∩ N is either horizontal, pseudohorizontal, vertical or pseudovertical
Graph Manifolds And Taut Foliations
- J. DIFFERENTIAL GEOM
, 1997
"... We examine the existence of foliations without Reeb components, taut foliations, and foliations with no S¹ x S¹-leaves, among graph manifolds. We show that each condition is strictly stronger than its predecessor(s), in the strongest possible sense; there are manifolds admitting foliations of eac ..."
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Cited by 14 (7 self)
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We examine the existence of foliations without Reeb components, taut foliations, and foliations with no S¹ x S¹-leaves, among graph manifolds. We show that each condition is strictly stronger than its predecessor(s), in the strongest possible sense; there are manifolds admitting foliations
Profinite properties of graph manifolds
, 2009
"... Let M be a closed, orientable, irreducible, geometrizable 3-manifold. We prove that the profinite topology on the fundamental group of π1(M) is efficient with respect to the JSJ decomposition of M. We go on to prove that π1(M) is good, in the sense of Serre, if all the pieces of the JSJ decompositio ..."
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Cited by 8 (3 self)
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decomposition are. We also prove that if M is a graph manifold then π1(M) is conjugacy separable. A group G is conjugacy separable if every conjugacy class is closed in the profinite topology on G. This can be thought of as a strengthening of residual finiteness (which is equivalent to the trivial subgroup’s
Graph manifolds with boundary are virtually special
, 2013
"... Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in π1M, and that the double cosets for crossing surfaces are also separable. We deduce that if there is a ‘sufficient ’ collection of surfaces in M, then π1M is virtually the fundamenta ..."
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Cited by 18 (4 self)
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Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in π1M, and that the double cosets for crossing surfaces are also separable. We deduce that if there is a ‘sufficient ’ collection of surfaces in M, then π1M is virtually
STABILIZATIONS OF HEEGAARD SPLITTINGS OF GRAPH MANIFOLDS
, 2008
"... We show that after one stabilization, a strongly irreducible Heegaard splitting of suitably large genus of a graph manifold is isotopic to an amalgamation along a modified version of the system of canonical tori in the JSJ decomposition. As a corollary, two strongly irreducible Heegaard splittings ..."
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We show that after one stabilization, a strongly irreducible Heegaard splitting of suitably large genus of a graph manifold is isotopic to an amalgamation along a modified version of the system of canonical tori in the JSJ decomposition. As a corollary, two strongly irreducible Heegaard
On the geometric and algebraic rank of graph manifolds
, 2003
"... Abstract. For any n ∈ N we construct graph manifolds of genus 4n that have 3n-generated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3-manifold 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 3n-generated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3-manifold M is an embedded orientable surface S such that M − S consists of 2 handlebodies V1 and V2. This decomposition of M
Zn-manifolds in 4-dimensional graph-manifolds
, 2005
"... A standard fact about two incompressible surfaces in an irreducible 3-manifold is that one can move one of them by isotopy so that their intersection becomes π1-injective. By extending it on the maps of some 3-dimensional Zn-manifolds into 4-manifolds, we prove that any homotopy equivalence of 4-dim ..."
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-dimensional graph-manifolds with reduced graph-structures is homotopic to a diffeomorphism preserving the structures.
Quasi-isometric classification of graph manifold groups
- DUKE MATH. J
"... We show that the fundamental groups of any two closed irreducible non-geometric graph-manifolds are quasi-isometric. This answers a question of Kapovich and Leeb. We also classify the quasi-isometry types of fundamental groups of graph-manifolds with boundary in terms of certain finite two-colored ..."
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Cited by 25 (5 self)
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We show that the fundamental groups of any two closed irreducible non-geometric graph-manifolds are quasi-isometric. This answers a question of Kapovich and Leeb. We also classify the quasi-isometry types of fundamental groups of graph-manifolds with boundary in terms of certain finite two
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