Mostrando recursos 1 - 20 de 1.015

  1. Describing the universal cover of a noncompact limit

    Ennis, John; Wei, Guofang
    Suppose that [math] is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds [math] with a uniform lower bound on Ricci curvature. In a previous paper the authors showed that when [math] is compact the universal cover [math] is a quotient of the Gromov–Hausdorff limit of the universal covers [math] . This is not true when [math] is noncompact. In this paper we introduce the notion of pseudo-nullhomotopic loops and give a description of the universal cover of a noncompact limit space in terms of the covering spaces of balls of increasing size in the sequence.

  2. Algebraic and geometric convergence of discrete representations into $\mathrm{PSL}_2\mathbb{C}$

    Biringer, Ian; Souto, Juan
    Anderson and Canary have shown that if the algebraic limit of a sequence of discrete, faithful representations of a finitely generated group into [math] does not contain parabolics, then it is also the sequence’s geometric limit. We construct examples that demonstrate the failure of this theorem for certain sequences of unfaithful representations, and offer a suitable replacement.

  3. Circle homeomorphisms and shears

    Šarić, Dragomir
    We give parameterizations of homeomorphisms, quasisymmetric maps and symmetric maps of the unit circle in terms of shear coordinates for the Farey tesselation.

  4. Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms

    Sorrentino, Alfonso; Viterbo, Claude
    In this article we prove that for a smooth fiberwise convex Hamiltonian, the asymptotic Hofer distance from the identity gives a strict upper bound to the value at 0 of Mather’s [math] function, thus providing a negative answer to a question asked by Siburg [Duke Math. J. 92 (1998) 295-319]. However, we show that equality holds if one considers the asymptotic distance defined in Viterbo [Math. Ann. 292 (1992) 685-710].

  5. Adams operations in smooth $K$–theory

    Bunke, Ulrich
    We show that the Adams operation [math] , [math] , in complex [math] –theory lifts to an operation [math] in smooth [math] –theory. If [math] is a [math] –oriented vector bundle with Thom isomorphism [math] , then there is a characteristic class [math] such that [math] in [math] for all [math] . We lift this class to a [math] –valued characteristic class for real vector bundles with geometric [math] –structures. ¶ If [math] is a [math] –oriented proper submersion, then for all [math] we have [math] in [math] , where [math] is the stable [math] –oriented normal bundle of [math] ....

  6. Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures

    Gompf, Robert E; Scharlemann, Martin; Thompson, Abigail
    If there are any [math] –component counterexamples to the Generalized Property R Conjecture, a least genus component of all such counterexamples cannot be a fibered knot. Furthermore, the monodromy of a fibered component of any such counterexample has unexpected restrictions. ¶ The simplest plausible counterexample to the Generalized Property R Conjecture could be a [math] –component link containing the square knot. We characterize all two-component links that contain the square knot and which surger to [math] . We exhibit a family of such links that are probably counterexamples to Generalized Property R. These links can be used to generate slice knots that are not...

  7. Correction to “A cartesian presentation of weak $n$–categories”

    Rezk, Charles
    This paper gives a corrected proof for Proposition 6.6 of “A Cartesian presentation of weak [math] –categories” [Geom. Topol. 14 (2010) 521–571] by the author.

  8. On the classification of gradient Ricci solitons

    Petersen, Peter; Wylie, William
    We show that the only shrinking gradient solitons with vanishing Weyl tensor and Ricci tensor satisfying a weak integral condition are quotients of the standard ones [math] , [math] and [math] . This gives a new proof of the Hamilton–Ivey–Perelman classification of [math] –dimensional shrinking gradient solitons. We also show that gradient solitons with constant scalar curvature and suitably decaying Weyl tensor when noncompact are quotients of [math] , [math] , [math] , [math] or [math] .

  9. Twist-rigid Coxeter groups

    Caprace, Pierre-Emmanuel; Przytycki, Piotr
    We prove that two angle-compatible Coxeter generating sets of a given finitely generated Coxeter group are conjugate provided one of them does not admit any elementary twist. This confirms a basic case of a general conjecture which describes a potential solution to the isomorphism problem for Coxeter groups.

  10. Relative rounding in toric and logarithmic geometry

    Nakayama, Chikara; Ogus, Arthur
    We show that the introduction of polar coordinates in toric geometry smoothes a wide class of equivariant mappings, rendering them locally trivial in the topological category. As a consequence, we show that the Betti realization of a smooth proper and exact mapping of log analytic spaces is a topological fibration, whose fibers are orientable manifolds (possibly with boundary). This turns out to be true even for certain noncoherent log structures, including some families familiar from mirror symmetry. The moment mapping plays a key role in our proof.

  11. The rational homology of spaces of long knots in codimension $\gt 2$

    Lambrechts, Pascal; Turchin, Victor; Volić, Ismar
    We determine the rational homology of the space of long knots in [math] for [math] . Our main result is that the Vassiliev spectral sequence computing this rational homology collapses at the [math] page. As a corollary we get that the homology of long knots (modulo immersions) is the Hochschild homology of the Poisson algebras operad with bracket of degree [math] , which can be obtained as the homology of an explicit graph complex and is in theory completely computable. ¶ Our proof is a combination of a relative version of Kontsevich’s formality of the little [math] –disks operad and of...

  12. Espace des modules marqués des surfaces projectives convexes de volume fini

    Marquis, Ludovic
    Cet article est la suite de l’article [arXiv :0902.3143] dans lequel l’auteur caractérisait le fait d’être de volume fini pour une surface projective convexe. On montre ici que l’espace des modules [math] des structures projectives convexes de volume fini sur la surface [math] de genre [math] à [math] pointes est homéomorphe à [math] . ¶ Enfin, on montre que [math] s’identifie à une composante connexe de l’espace des représentations du groupe fondamental de [math] dans [math] qui conservent les paraboliques à conjugaison près. ¶ This article follows the article [arXiv :0902.3143] in which the author characterizes the fact of being of finite volume for...

  13. Planar open books, monodromy factorizations and symplectic fillings

    Plamenevskaya, Olga; Van Horn-Morris, Jeremy
    We study fillings of contact structures supported by planar open books by analyzing positive factorizations of their monodromy. Our method is based on Wendl’s theorem on symplectic fillings of planar open books. We prove that every virtually overtwisted contact structure on [math] has a unique filling, and describe fillable and nonfillable tight contact structures on certain Seifert fibered spaces.

  14. Homotopy groups of the moduli space of metrics of positive scalar curvature

    Botvinnik, Boris; Hanke, Bernhard; Schick, Thomas; Walsh, Mark
    We show by explicit examples that in many degrees in a stable range the homotopy groups of the moduli spaces of Riemannian metrics of positive scalar curvature on closed smooth manifolds can be non-trivial. This is achieved by further developing and then applying a family version of the surgery construction of Gromov–Lawson to certain nonlinear smooth sphere bundles constructed by Hatcher.

  15. Perturbative invariants of 3–manifolds with the first Betti number 1

    Ohtsuki, Tomotada
    It is known that perturbative invariants of rational homology 3–spheres can be constructed by using arithmetic perturbative expansion of quantum invariants of them. However, we could not make arithmetic perturbative expansion of quantum invariants for 3–manifolds with positive Betti numbers by the same method. ¶ In this paper, we explain how to make arithmetic perturbative expansion of quantum [math] invariants of 3–manifolds with the first Betti number [math] . Further, motivated by this expansion, we construct perturbative invariants of such 3–manifolds. We show some properties of the perturbative invariants, which imply that their coefficients are independent invariants.

  16. The Maskit embedding of the twice punctured torus

    Series, Caroline
    The Maskit embedding [math] of a surface [math] is the space of geometrically finite groups on the boundary of quasifuchsian space for which the “top” end is homeomorphic to [math] , while the “bottom” end consists of triply punctured spheres, the remains of [math] when a set of pants curves have been pinched. As such representations vary in the character variety, the conformal structure on the top side varies over the Teichmüller space [math] . ¶ We investigate [math] when [math] is a twice punctured torus, using the method of pleating rays. Fix a projective measure class [math] supported on closed...

  17. Bounds on exceptional Dehn filling II

    Agol, Ian
    We show that there are at most finitely many one cusped orientable hyperbolic [math] –manifolds which have more than eight nonhyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.

  18. Heegaard surfaces and the distance of amalgamation

    Li, Tao
    Let [math] and [math] be orientable irreducible [math] –manifolds with connected boundary and suppose [math] . Let [math] be a closed [math] –manifold obtained by gluing [math] to [math] along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then [math] is not homeomorphic to [math] and all small-genus Heegaard splittings of [math] are standard in a certain sense. In particular, [math] , where [math] denotes the Heegaard genus of [math] . This theorem is also true for certain manifolds with multiple boundary components.

  19. Morita classes in the homology of automorphism groups of free groups

    Conant, James; Vogtmann, Karen
    Using Kontsevich’s identification of the homology of the Lie algebra [math] with the cohomology of [math] , Morita defined a sequence of [math] –dimensional classes [math] in the unstable rational homology of [math] . He showed by a computer calculation that the first of these is non-trivial, so coincides with the unique non-trivial rational homology class for [math] . Using the “forested graph complex" introduced in an earlier paper, we reinterpret and generalize Morita’s cycles, obtaining an unstable cycle for every connected odd-valent graph. (Morita has independently found similar generalizations of these cycles.) The description of Morita’s original cycles becomes...

  20. Limit groups and groups acting freely on $\mathbb{R}^n$–trees

    Guirardel, Vincent
    We give a simple proof of the finite presentation of Sela’s limit groups by using free actions on [math] –trees. We first prove that Sela’s limit groups do have a free action on an [math] –tree. We then prove that a finitely generated group having a free action on an [math] –tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic groups. As a corollary, such a group is finitely presented, has a finite classifying space, its abelian subgroups are finitely generated and contains only finitely many conjugacy...

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