Výsledky vyhledávání - "Daryl Cooper"

Degenerations of representations and thin triangles

Autor: Daryl Cooper

There is a compactification of the space of representations of a finitely generated group into the groups of isometries of all spaces with $\Delta$-thin triangles. The ideal points are actions on $\mathbb R$-trees. It is a geometric reformulation and

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The area of convex projective surfaces and Fock–Goncharov coordinates

Autor: Daryl Cooper, Ilesanmi Adeboye

Publikováno v: Journal of Topology and Analysis. 12:533-546

The area of a convex projective surface of genus [Formula: see text] is at least [Formula: see text] where [Formula: see text] is the vector of triangle invariants of Bonahon–Dreyer and [Formula: see text] are the Fock–Goncharov triple ratios.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f0c106f37362b9348bf6f75f1f82aee1
https://doi.org/10.1142/s1793525319500560

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Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic $3$–manifolds

Autor: Daryl Cooper, David Futer

Publikováno v: Geom. Topol. 23, no. 1 (2019), 241-298

This paper proves that every finite volume hyperbolic 3-manifold M contains a ubiquitous collection of closed, immersed, quasi-Fuchsian surfaces. These surfaces are ubiquitous in the sense that their preimages in the universal cover separate any pair

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88b91776cf0ece037e7e21e7cc1b7315
https://projecteuclid.org/euclid.gt/1552356082

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Deforming convex projective manifolds

Autor: Stephan Tillmann, Darren D. Long, Daryl Cooper

Publikováno v: Cooper, D; Long, D; & Tillmann, S. (2018). Deforming convex projective manifolds. Geometry and Topology, 22(3), 1349-1404. doi: 10.2140/gt.2018.22.1349. UC Santa Barbara: Retrieved from: http://www.escholarship.org/uc/item/7160t8q9
Geometry & Topology, vol 22, iss 3
Geometry and Topology, vol 22, iss 3
Geom. Topol. 22, no. 3 (2018), 1349-1404

We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact manifold

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http://www.escholarship.org/uc/item/7160t8q9

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The Heisenberg group acts on a strictly convex domain

Autor: Daryl Cooper

Publikováno v: Conformal Geometry and Dynamics of the American Mathematical Society, vol 21, iss 4
Cooper, D. (2017). The Heisenberg group acts on a strictly convex domain. Conformal Geometry and Dynamics, 21(4), 101-104. doi: 10.1090/ecgd/307. UC Santa Barbara: Retrieved from: http://www.escholarship.org/uc/item/16x4p858
Conformal Geometry and Dynamics, vol 21, iss 4

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https://escholarship.org/uc/item/16x4p858

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Generalized Cusps in Real Projective Manifolds: Classification

Autor: Arielle Leitner, Samuel A. Ballas, Daryl Cooper

A generalized cusp $C$ is diffeomorphic to $[0,\infty)$ times a closed Euclidean manifold. Geometrically $C$ is the quotient of a properly convex domain by a lattice, $\Gamma$, in one of a family of affine groups $G(\psi)$, parameterized by a point $

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Non-faithful representations of surface groups into $$ SL (2,\mathbb C)$$ S L ( 2 , C ) which kill no simple closed curve

Autor: Jason Fox Manning, Daryl Cooper

Publikováno v: Geometriae Dedicata. 177:165-187

We give counterexamples to a version of the simple loop conjecture in which the target group is $$ PSL (2,\mathbb C)$$ . These examples answer a question of Minsky in the negative.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::207e7180e308ac795e7edffa4373a4ff
https://doi.org/10.1007/s10711-014-9984-0

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A generalization of the Epstein-Penner construction to projective manifolds

Autor: Darren D. Long, Daryl Cooper

Publikováno v: Cooper, D; & Long, DD. (2015). A generalization of the Epstein-Penner construction to projective manifolds. Proceedings of the American Mathematical Society, 143(10), 4561-4569. doi: 10.1090/S0002-9939-2015-12579-8. UC Santa Barbara: Retrieved from: http://www.escholarship.org/uc/item/1176p70q
Proceedings of the American Mathematical Society, vol 143, iss 10

We extend the canonical cell decomposition due to Epstein and Penner of a hyperbolic manifold with cusps to the strictly convex setting. It follows that a sufficiently small deformation of the holonomy of a finite volume strictly convex real projecti

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c5df7ab36333177d05bbcbb77d119275
http://www.escholarship.org/uc/item/1176p70q

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Finite-volume hyperbolic 3–manifolds contain immersed quasi-Fuchsian surfaces

Autor: Mark D. Baker, Daryl Cooper

Publikováno v: Algebraic and Geometric Topology
Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2015, 15 (2), pp.1199-1228. 〈10.2140/agt.2015.15.1199〉
Algebraic and Geometric Topology, vol 15, iss 2
Algebraic and Geometric Topology, 2015, 15 (2), pp.1199-1228. ⟨10.2140/agt.2015.15.1199⟩
Baker, MD; & Cooper, D. (2015). Finite-volume hyperbolic 3–manifolds contain immersed quasi-Fuchsian surfaces. Algebraic and Geometric Topology, 15(2), 1199-1228. doi: 10.2140/agt.2015.15.1199. UC Santa Barbara: Retrieved from: http://www.escholarship.org/uc/item/0qz4002x
Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2015, 15 (2), pp.1199-1228. ⟨10.2140/agt.2015.15.1199⟩
Algebraic & Geometric Topology, vol 15, iss 2
Algebr. Geom. Topol. 15, no. 2 (2015), 1199-1228

The paper contains a new proof that a complete, non-compact hyperbolic $3$-manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface.
Comment: Final version to appear in AGT. Some typos corrected, particularly def (3.6

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::331f852c075ea441f518fe81350b2320
https://hal.archives-ouvertes.fr/hal-01059307

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Computing Varieties of Representations of Hyperbolic 3-Manifolds into SL(4, ℝ)

Autor: Daryl Cooper, Darren D. Long, Morwen Thistlethwaite

Publikováno v: Experimental Mathematics. 15:291-305

The geometric structure on a closed orientable hyperbolic 3- manifold determines a discrete faithful representation ρ of its fundamental group into SO+(3, 1), unique up to conjugacy. Although Mostow rigidity prohibits us from deforming ρ, we can tr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::fd9410dd3b86536fbcb56278bc38f6f5
https://doi.org/10.1080/10586458.2006.10128965

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