The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform
Pedro Ontaneda - One of the best experts on this subject based on the ideXlab platform.
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the moduli space of negatively curved metrics of a Hyperbolic Manifold
Journal of Topology, 2010Co-Authors: F T Farrell, Pedro OntanedaAbstract:We prove that the moduli space of negatively curved metrics of a Hyperbolic Manifold M n has nontrivial homotopy and homology groups in certain dimensions (depending on n) provided M has a ‘good’ closed geodesic.
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the teichmuller space of pinched negatively curved metrics on a Hyperbolic Manifold is not contractible
Annals of Mathematics, 2009Co-Authors: Thomas F Farrell, Pedro OntanedaAbstract:For a smooth Manifold M we define the Teichmuller space 2T(M) of all Riemannian metrics on M and the Teichmuller space 2T€(M) of € -pinched negatively curved metrics on M, where 0 < € < oo. We prove that if M is Hyperbolic, the natural inclusion ?f€(M) <-+ 2T(M) is, in general, not homotopically trivial. In particular, 2T€(M) is, in general, not contractible.
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the double of a Hyperbolic Manifold and non positively curved exotic pl structures
Transactions of the American Mathematical Society, 2002Co-Authors: Pedro OntanedaAbstract:We give examples of non-compact finite volume real Hyperbolic Manifolds of dimension greater than five, such that their doubles admit at least three non-equivalent smoothable PL structures, two of which admit a Riemannian metric of non-positive curvature while the third does not. We also prove that the doubles of non-compact finite volume real Hyperbolic Manifolds of dimension greater than four are differentiably rigid.
Jinsung Park - One of the best experts on this subject based on the ideXlab platform.
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eta invariant and selberg zeta function of odd type over convex co compact Hyperbolic Manifolds
Advances in Mathematics, 2010Co-Authors: Colin Guillarmou, Sergiu Moroianu, Jinsung ParkAbstract:Abstract We show meromorphic extension and give a complete description of the divisors of a Selberg zeta function of odd type Z Γ , Σ o ( λ ) associated to the spinor bundle Σ on an odd dimensional convex co-compact Hyperbolic Manifold Γ \ H 2 n + 1 . As a byproduct we do a full analysis of the spectral and scattering theory of the Dirac operator on asymptotically Hyperbolic Manifolds. We show that there is a natural eta invariant η ( D ) associated to the Dirac operator D over a convex co-compact Hyperbolic Manifold Γ \ H 2 n + 1 and that exp ( π i η ( D ) ) = Z Γ , Σ o ( 0 ) , thus extending Millson's formula to this setting. Under some assumption on the exponent of convergence of Poincare series for the group Γ, we also define an eta invariant for the odd signature operator, and we show that for Schottky 3-dimensional Hyperbolic Manifolds it gives the argument of a holomorphic function which appears in the Zograf factorization formula relating two natural Kahler potentials for Weil–Petersson metric on Schottky space.
Thomas F Farrell - One of the best experts on this subject based on the ideXlab platform.
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the teichmuller space of pinched negatively curved metrics on a Hyperbolic Manifold is not contractible
Annals of Mathematics, 2009Co-Authors: Thomas F Farrell, Pedro OntanedaAbstract:For a smooth Manifold M we define the Teichmuller space 2T(M) of all Riemannian metrics on M and the Teichmuller space 2T€(M) of € -pinched negatively curved metrics on M, where 0 < € < oo. We prove that if M is Hyperbolic, the natural inclusion ?f€(M) <-+ 2T(M) is, in general, not homotopically trivial. In particular, 2T€(M) is, in general, not contractible.
Hongbin Sun - One of the best experts on this subject based on the ideXlab platform.
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non lerfness of arithmetic Hyperbolic Manifold groups and mixed 3 Manifold groups
Duke Mathematical Journal, 2019Co-Authors: Hongbin SunAbstract:We will show that for any noncompact arithmetic Hyperbolic m-Manifold with m>3, and any compact arithmetic Hyperbolic m-Manifold with m>4 that is not a 7-dimensional one defined by octonions, its fundamental group is not locally extended residually finite (LERF). The main ingredient in the proof is a study on abelian amalgamations of Hyperbolic 3-Manifold groups. We will also show that a compact orientable irreducible 3-Manifold with empty or tori boundary supports a geometric structure if and only if its fundamental group is LERF.
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geometrically finite amalgamations of Hyperbolic 3 Manifold groups are not lerf
Proceedings of The London Mathematical Society, 2019Co-Authors: Hongbin SunAbstract:We prove that, for any two finite volume Hyperbolic $3$-Manifolds, the amalgamation of their fundamental groups along any nontrivial geometrically finite subgroup is not LERF. This generalizes the author's previous work on nonLERFness of amalgamations of Hyperbolic $3$-Manifold groups along abelian subgroups. A consequence of this result is that closed arithmetic Hyperbolic $4$-Manifolds have nonLERF fundamental groups. Along with the author's previous work, we get that, for any arithmetic Hyperbolic Manifold with dimension at least $4$, with possible exceptions in $7$-dimensional Manifolds defined by the octonion, its fundamental group is not LERF.
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nonlerfness of arithmetic Hyperbolic Manifold groups
arXiv: Geometric Topology, 2016Co-Authors: Hongbin SunAbstract:We will show that, for any noncompact arithmetic Hyperbolic $m$-Manifold with $m\geq 4$, and any compact arithmetic Hyperbolic $m$-Manifold with $m\geq 5$ which is not a $7$-dimensional arithmetic Hyperbolic Manifold defined by octonions, its fundamental group is not LERF. The main ingredient in the proof is a study of certain graph of groups with Hyperbolic $3$-Manifold groups being the vertex groups. We will also show that a compact irreducible $3$-Manifold with empty or tori boundary does not support a geometric structure if and only if its fundamental group is not LERF.
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nonlerfness of arithmetic Hyperbolic Manifold groups and mixed 3 Manifold groups
arXiv: Geometric Topology, 2016Co-Authors: Hongbin SunAbstract:We will show that, for any noncompact arithmetic Hyperbolic $m$-Manifold with $m> 3$, and any compact arithmetic Hyperbolic $m$-Manifold with $m> 4$ that is not a $7$-dimensional arithmetic Hyperbolic Manifold defined by octonions, its fundamental group is not LERF. The main ingredient in the proof is a study on abelian amalgamations of Hyperbolic $3$-Manifold groups. We will also show that a compact orientable irreducible $3$-Manifold with empty or tori boundary supports a geometric structure if and only if its fundamental group is LERF.
Evangelos I Sfakianakis - One of the best experts on this subject based on the ideXlab platform.
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angular inflation in multi field alpha attractors
Journal of Cosmology and Astroparticle Physics, 2019Co-Authors: Perseas Christodoulidis, Diederik Roest, Evangelos I SfakianakisAbstract:We explore the dynamics of multi-field models of inflation in which the field-space metric is a Hyperbolic Manifold of constant curvature. Such models are known as α-attractors and their single-field regimes have been extensively studied in the context of inflation and supergravity. We find a variety of multi-field inflationary trajectories in different regions of parameter space, which is spanned by the mass parameters and the Hyperbolic curvature. Amongst these is a novel dynamical attractor along the boundary of the Poincare disc which we dub "angular inflation". We calculate the evolution of adiabatic and isocurvature fluctuations during this regime and show that, while isocurvature modes decay during this phase, the duration of the angular inflation period can shift the single-field predictions of α-attractors. For highly curved field-space Manifolds, this can lead to predictions that lie outside the current observational bounds.
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angular inflation in multi field alpha attractors
arXiv: High Energy Physics - Theory, 2018Co-Authors: Perseas Christodoulidis, Diederik Roest, Evangelos I SfakianakisAbstract:We explore the dynamics of multi-field models of inflation in which the field-space metric is a Hyperbolic Manifold of constant curvature. Such models are known as $\alpha$-attractors and their single-field regimes have been extensively studied in the context of inflation and supergravity. We find a variety of multi-field inflationary trajectories in different regions of parameter space, which is spanned by the mass parameters and the Hyperbolic curvature. Amongst these is a novel dynamical attractor along the boundary of the Poincare disc which we dub "angular inflation". We calculate the evolution of adiabatic and isocurvature fluctuations during this regime and show that, while isocurvature modes decay during this phase, the duration of the angular inflation period can shift the single-field predictions of $\alpha$-attractors.
