Harmonic maps $\mathbf {M^3 \rightarrow S^1}$ and 2-cycles, realizing the Thurston norm
نویسندگان
چکیده
منابع مشابه
The Thurston Norm
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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Cochran introduced Alexander polynomials over non–commutative Laurent polynomial rings. Their degrees were studied by Cochran, Harvey and Turaev as they give lower bounds on the Thurston norm. We first extend Cochran’s definition to twisted Alexander polynomials. We then show how Reidemeister torsion relates to these invariants and we give lower bounds on the Thurston norm in terms of the Reide...
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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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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 multi-variable Alexander polynomial. To illustrate these techniques, we also compute the Thurston polytopes of several specific link complements.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03577-9