Mostrando recursos 1 - 20 de 76

  1. Index


  2. Index


  3. Lifting Homeomorphisms and Cyclic Branched Covers of Spheres

    Ghaswala, Tyrone; Winarski, Rebecca R.
    We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This answers the question that appeared in an early version of the erratum of Birman and Hilden [2].

  4. Lifting Homeomorphisms and Cyclic Branched Covers of Spheres

    Ghaswala, Tyrone; Winarski, Rebecca R.
    We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This answers the question that appeared in an early version of the erratum of Birman and Hilden [2].

  5. A Remark on $\operatorname{Pin}(2)$ -Equivariant Floer Homology

    Stoffregen, Matthew
    In this remark, we show how the monopole Frøyshov invariant, as well as the analogues of the Involutive Heegaard Floer correction terms $\underline{d},\bar{d}$ , are related to the $\operatorname{Pin}(2)$ -equivariant Floer homology $\mathit{SWFH}^{G}_{*}$ . We show that the only interesting correction terms of a $\operatorname{Pin}(2)$ -space are those coming from the subgroups $\mathbb{Z}/4$ , $S^{1}$ , and $\operatorname{Pin}(2)$ itself.

  6. A Remark on $\operatorname{Pin}(2)$ -Equivariant Floer Homology

    Stoffregen, Matthew
    In this remark, we show how the monopole Frøyshov invariant, as well as the analogues of the Involutive Heegaard Floer correction terms $\underline{d},\bar{d}$ , are related to the $\operatorname{Pin}(2)$ -equivariant Floer homology $\mathit{SWFH}^{G}_{*}$ . We show that the only interesting correction terms of a $\operatorname{Pin}(2)$ -space are those coming from the subgroups $\mathbb{Z}/4$ , $S^{1}$ , and $\operatorname{Pin}(2)$ itself.

  7. A Coarse Stratification of the Monster Tower

    Castro, Alex; Colley, Susan Jane; Kennedy, Gary; Shanbrom, Corey
    The monster tower is a tower of spaces over a specified base; each space in the tower is a parameter space for curvilinear data up to a specified order. We describe and analyze a natural stratification of these spaces.

  8. A Coarse Stratification of the Monster Tower

    Castro, Alex; Colley, Susan Jane; Kennedy, Gary; Shanbrom, Corey
    The monster tower is a tower of spaces over a specified base; each space in the tower is a parameter space for curvilinear data up to a specified order. We describe and analyze a natural stratification of these spaces.

  9. Hodge Integrals in FJRW Theory

    Guéré, Jérémy
    We study higher-genus Fan–Jarvis–Ruan–Witten theory of any chain polynomial with any group of symmetries. Precisely, we give an explicit way to compute the cup product of Polishchuk and Vaintrob’s virtual class with the top Chern class of the Hodge bundle. Our formula for this product holds in any genus and without any assumption on the semi-simplicity of the underlying cohomological field theory.

  10. Hodge Integrals in FJRW Theory

    Guéré, Jérémy
    We study higher-genus Fan–Jarvis–Ruan–Witten theory of any chain polynomial with any group of symmetries. Precisely, we give an explicit way to compute the cup product of Polishchuk and Vaintrob’s virtual class with the top Chern class of the Hodge bundle. Our formula for this product holds in any genus and without any assumption on the semi-simplicity of the underlying cohomological field theory.

  11. Circle-Valued Morse Theory for Frame Spun Knots and Surface-Links

    Endo, Hisaaki; Pajitnov, Andrei
    Let $N^{k}\subset S^{k+2}$ be a closed oriented submanifold. Denote its complement by $C(N)=S^{k+2}\setminus N$ . Denote by $\xi\in H^{1}(C(N))$ the class dual to $N$ . The Morse–Novikov number of $C(N)$ is by definition the minimal possible number of critical points of a regular Morse map $C(N)\to S^{1}$ belonging to $\xi$ . In the first part of this paper, we study the case where $N$ is the twist frame spun knot associated with an $m$ -knot $K$ . We obtain a formula that relates the Morse–Novikov numbers of $N$ and $K$ and generalizes the classical results of D. Roseman and E....

  12. Circle-Valued Morse Theory for Frame Spun Knots and Surface-Links

    Endo, Hisaaki; Pajitnov, Andrei
    Let $N^{k}\subset S^{k+2}$ be a closed oriented submanifold. Denote its complement by $C(N)=S^{k+2}\setminus N$ . Denote by $\xi\in H^{1}(C(N))$ the class dual to $N$ . The Morse–Novikov number of $C(N)$ is by definition the minimal possible number of critical points of a regular Morse map $C(N)\to S^{1}$ belonging to $\xi$ . In the first part of this paper, we study the case where $N$ is the twist frame spun knot associated with an $m$ -knot $K$ . We obtain a formula that relates the Morse–Novikov numbers of $N$ and $K$ and generalizes the classical results of D. Roseman and E....

  13. The McKay Correspondence, Tilting, and Rationality

    Brown, Morgan; Shipman, Ian
    We consider the problem of comparing $t$ -structures under the derived McKay correspondence and for tilting equivalences. In low-dimensional cases, we relate the $t$ -structures via torsion theories arising from additive functions on the triangulated category. As an application, we give a criterion for rationality for surfaces with a tilting bundle. We also show that every smooth projective surface that admits a full, strong, and exceptional collection of line bundles is rational.

  14. The McKay Correspondence, Tilting, and Rationality

    Brown, Morgan; Shipman, Ian
    We consider the problem of comparing $t$ -structures under the derived McKay correspondence and for tilting equivalences. In low-dimensional cases, we relate the $t$ -structures via torsion theories arising from additive functions on the triangulated category. As an application, we give a criterion for rationality for surfaces with a tilting bundle. We also show that every smooth projective surface that admits a full, strong, and exceptional collection of line bundles is rational.

  15. Linear Spaces on Hypersurfaces over Number Fields

    Brandes, Julia
    We establish an analytic Hasse principle for linear spaces of affine dimension $m$ on a complete intersection over an algebraic field extension $\mathbb{K}$ of $\mathbb{Q}$ . The number of variables required to do this is no larger than what is known for the analogous problem over $\mathbb{Q}$ . As an application, we show that any smooth hypersurface over $\mathbb{K}$ whose dimension is large enough in terms of the degree is $\mathbb{K}$ -unirational, provided that either the degree is odd or $\mathbb{K}$ is totally imaginary.

  16. Linear Spaces on Hypersurfaces over Number Fields

    Brandes, Julia
    We establish an analytic Hasse principle for linear spaces of affine dimension $m$ on a complete intersection over an algebraic field extension $\mathbb{K}$ of $\mathbb{Q}$ . The number of variables required to do this is no larger than what is known for the analogous problem over $\mathbb{Q}$ . As an application, we show that any smooth hypersurface over $\mathbb{K}$ whose dimension is large enough in terms of the degree is $\mathbb{K}$ -unirational, provided that either the degree is odd or $\mathbb{K}$ is totally imaginary.

  17. Classification Problem of Holomorphic Isometries of the Unit Disk Into Polydisks

    Chan, Shan Tai
    We study the classification problem of holomorphic isometric embeddings of the unit disk into polydisks as in [Ng10, Ch16a]. We give a complete classification of all such holomorphic isometries when the target is the $4$ -disk $\Delta^{4}$ . Moreover, we classify those holomorphic isometric embeddings with certain prescribed sheeting numbers. In addition, we prove that a known example in the space $\mathbf{HI}_{k}(\Delta,\Delta^{qk};q)$ is globally rigid for any integers $k,q\ge2$ , which generalizes Theorem 1.1 in [Ch16a].

  18. Classification Problem of Holomorphic Isometries of the Unit Disk Into Polydisks

    Chan, Shan Tai
    We study the classification problem of holomorphic isometric embeddings of the unit disk into polydisks as in [Ng10, Ch16a]. We give a complete classification of all such holomorphic isometries when the target is the $4$ -disk $\Delta^{4}$ . Moreover, we classify those holomorphic isometric embeddings with certain prescribed sheeting numbers. In addition, we prove that a known example in the space $\mathbf{HI}_{k}(\Delta,\Delta^{qk};q)$ is globally rigid for any integers $k,q\ge2$ , which generalizes Theorem 1.1 in [Ch16a].

  19. Involution and Commutator Length for Complex Hyperbolic Isometries

    Paupert, Julien; Will, Pierre
    We study decompositions of complex hyperbolic isometries as products of involutions. We show that $\operatorname {PU}(2,1)$ has involution length 4 and commutator length 1 and that, for all $n\geqslant3$ , $\operatorname {PU}(n,1)$ has involution length at most 8.

  20. Involution and Commutator Length for Complex Hyperbolic Isometries

    Paupert, Julien; Will, Pierre
    We study decompositions of complex hyperbolic isometries as products of involutions. We show that $\operatorname {PU}(2,1)$ has involution length 4 and commutator length 1 and that, for all $n\geqslant3$ , $\operatorname {PU}(n,1)$ has involution length at most 8.

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