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71
Thurston norm and cosmetic surgeries
"... Abstract. Two Dehn surgeries on a knot are called cosmetic if they yield homeomorphic manifolds. For a nullhomologous knot with certain conditions on the Thurston norm of the ambient manifold, if the knot admits cosmetic surgeries, then the surgery coefficients are equal up to sign. ..."
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Abstract. Two Dehn surgeries on a knot are called cosmetic if they yield homeomorphic manifolds. For a nullhomologous knot with certain conditions on the Thurston norm of the ambient manifold, if the knot admits cosmetic surgeries, then the surgery coefficients are equal up to sign.
ALEXANDER AND THURSTON NORMS OF FIBERED
"... For a 3manifoldM, McMullen derived from the Alexander polynomial of M a norm on H1(M,R) called the Alexander norm. He showed that the Thurston norm is an upper bound for the Alexander norm. He asked if these two norms were the same when M fibers over the circle. Here, I give examples that show thi ..."
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For a 3manifoldM, McMullen derived from the Alexander polynomial of M a norm on H1(M,R) called the Alexander norm. He showed that the Thurston norm is an upper bound for the Alexander norm. He asked if these two norms were the same when M fibers over the circle. Here, I give examples that show
The Sutured Thurston Norm
, 2006
"... For sutured threemanifolds M, there is a sutured Thurston norm x s due to M. Scharlemann [10]. Here, we show how depth one foliations of M can be useful tools for computing this norm. This uses the relation of these foliations with fibrations of DM (the double of M along the manifold R ⊂ ∂M given b ..."
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Cited by 3 (0 self)
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For sutured threemanifolds M, there is a sutured Thurston norm x s due to M. Scharlemann [10]. Here, we show how depth one foliations of M can be useful tools for computing this norm. This uses the relation of these foliations with fibrations of DM (the double of M along the manifold R ⊂ ∂M given
LINK FLOER HOMOLOGY AND THE THURSTON NORM
, 2007
"... Abstract. We show that link Floer homology detects the Thurston norm of a link complement. As an application, we show that the Thurston polytope of an alternating link is dual to the Newton polytope of its multivariable Alexander polynomial. To illustrate these techniques, we also compute the Thurs ..."
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Cited by 12 (0 self)
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Abstract. We show that link Floer homology detects the Thurston norm of a link complement. As an application, we show that the Thurston polytope of an alternating link is dual to the Newton polytope of its multivariable Alexander polynomial. To illustrate these techniques, we also compute
Thurston norm revisited
, 2009
"... We study Thurston’s norm on the second homology of a 3manifold. The novelty of our approach consists in the use of methods of the C ∗algebra theory. Namely, for Stallings ’ fibration M with pseudoAnosov monodromy, we associate a C ∗algebra whose Ktheory gives rise to an algebraic number field K ..."
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We study Thurston’s norm on the second homology of a 3manifold. The novelty of our approach consists in the use of methods of the C ∗algebra theory. Namely, for Stallings ’ fibration M with pseudoAnosov monodromy, we associate a C ∗algebra whose Ktheory gives rise to an algebraic number field
ALEXANDER AND THURSTON NORMS OF GRAPH LINKS
, 2008
"... We show that the Alexander and Thurston norms are the same for all irreducible EisenbudNeumann graph links in homology 3spheres. These are the links obtained by splicing Seifert links in homology 3spheres together along tori. By combining this result with previous results, we prove that the two ..."
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Cited by 1 (0 self)
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We show that the Alexander and Thurston norms are the same for all irreducible EisenbudNeumann graph links in homology 3spheres. These are the links obtained by splicing Seifert links in homology 3spheres together along tori. By combining this result with previous results, we prove
A homological estimate for the Thurston norm
"... Abstract We establish a new homological lower bound for the Thurston norm on 1cohomology of 3manifolds. This generalizes previous results of C. McMullen, S. Harvey, and the author. We also establish an analogous lower bound for 1cohomology of 2dimensional CWcomplexes. AMS Classification 57M27, ..."
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Cited by 4 (0 self)
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Abstract We establish a new homological lower bound for the Thurston norm on 1cohomology of 3manifolds. This generalizes previous results of C. McMullen, S. Harvey, and the author. We also establish an analogous lower bound for 1cohomology of 2dimensional CWcomplexes. AMS Classification 57M27
The Thurston norm via Normal Surfaces
, 2007
"... To Bill Thurston on the occasion of his sixtieth birthday Abstract Given a triangulation of a closed, oriented, irreducible, atoroidal 3–manifold every oriented, incompressible surface may be isotoped into normal position relative to the triangulation. Such a normal oriented surface is then encoded ..."
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Cited by 6 (1 self)
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by the combinatorics of the triangulation, whose image under the homology map is the unit ball, B, of the Thurston norm. Applications of this approach include (1) an algorithm to compute B and hence the Thurston norm of any homology class, (2) an explicit exponential bound on the number of vertices of B in terms
The Thurston norm, fibered manifolds and twisted Alexander polynomials
, 2005
"... Every element in the first cohomology group of a 3–manifold is dual to embedded surfaces. The Thurston norm measures the minimal ‘complexity ’ of such surfaces. For instance the Thurston norm of a knot complement determines the genus of the knot in the 3–sphere. We show that the degrees of twisted A ..."
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Cited by 47 (25 self)
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Every element in the first cohomology group of a 3–manifold is dual to embedded surfaces. The Thurston norm measures the minimal ‘complexity ’ of such surfaces. For instance the Thurston norm of a knot complement determines the genus of the knot in the 3–sphere. We show that the degrees of twisted
Results 1  10
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71