Thurston norm minimizing surfaces and skein trees for links in $S\sp 3$
نویسندگان
چکیده
منابع مشابه
The Thurston Norm via Normal Surfaces
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 by non-negative integer weights, 14 for each 3–simplex, that describe how many copies of each oriented normal disc type there are. The Euler characteristic and homo...
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We define the Conway skein module (M) of ordered based links in a 3-manifold M . This module gives rise to (M)-valued invariants of usual links in M . We determine a basis of the Z[z]-module (Σ× [0,1])/Tor( (Σ× [0,1])), where Σ is the real projective plane or a surface with boundary. For cylinders over the Möbius strip or the projective plane, we derive special properties of the Conway skein mo...
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Suppose a 2-handle is attached to a compact orientable 3-manifold M along an annulus A contained in a subsurface N of a M . If N is compressible in M, but N -A is not, then the Thurston norm is unaffected. This generalizes a series of results due to Przytycki, Jaco, and Johannson. Following Thurston [Th],define the complexity X(S) of an oriented surface S to be -x(C), where C is the union of al...
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We study noncommutative C∗-algebras arising in geometric topology. Our object are Thurston’s norms on the second homology of Stallings’ fibrations. It is shown that Thurston’s norm is a matter of pure algebra, if one looks at the Bratteli diagram of an AF C∗-algebra attached to measured geodesic laminations on a compact surface of genus greater or equal to 2. This approach leads to computationa...
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Two Dehn surgeries on a knot are called cosmetic if they yield homeomorphic manifolds. For a null-homologous 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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1989
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1989-0969321-3