Search

Your search keyword '"Sozen, Yasar"' showing total 31 results
Start Over Author "Sozen, Yasar"
31 results on '"Sozen, Yasar"'

1. A note on Reidemeister Torsion of G-Anosov Representations

Author

Zeybek, Hatice and Sozen, Yasar

Subjects
Mathematics - Geometric Topology, 32G15, 57R30
Abstract

This article considers $G$-Anosov representations of a fixed closed oriented Riemann surface $\Sigma$ of genus at least $2$. Here, $G$ is the Lie group $\text{PSp}(2n,\mathbb{R}$), $\text{PSO}(n,n)$ or $\text{PSO}(n,n+1)$. It proves that Reidemeister torsion (R-torsion) associated to $\Sigma$ with coefficients in the adjoint bundle representations of such representations is well-defined. Moreover, by using symplectic chain complex method, it establishes a novel formula for R-torsion of such representations in terms of the Atiyah-Bott-Goldman symplectic form corresponding to the Lie group $G$. Furtermore, it applies the results to Hitchin components, in particular, Teichm\"{u}ller space., Comment: 14 pages , 2 figures

Published
2021

4. Reidemeister torsion of a symplcetic complex

Author

Sozen, Yasar

Subjects
Mathematics - Geometric Topology, Mathematical Physics, 15A90, 57M99
Abstract

We consider a claim mentioned in \cite{Witten} pp 187 about the relation between a symplectic chain complex with $\omega-$compatible bases and Reidemeister Torsion of it. This is an explanation of it., Comment: 15 pages

Published
2004

5. Variation of the Liouville measure of a hyperbolic surface

Author

Bonahon, Francis and Sozen, Yasar

Subjects
Mathematics - Dynamical Systems, Mathematics - Geometric Topology, 32G15
Abstract

For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the riemannian metric defines a natural transverse measure to this foliation, the Liouville transverse measure, which does depend on the metric. For a surface S, we show that the map which to a hyperbolic metric on S associates its Liouville transverse measure is differentiable, in an appropriate sense. Its tangent map is valued in the space of transverse Holder distributions for the geodesic foliation., Comment: AmsLaTeX with package epsfig, 27 pages, 3 figures; one argument corrected in Section 7, minor improvements elsewhere; to appear in Erg. Th. Dyn. Syst

Published
2002
Full Text
View/download PDF

7. A note on parabolic difference equations on manifold.

Author

Ashyralyev, Allaberen, Hezenci, Fatih, and Sozen, Yasar

Subjects
NUMERICAL solutions to boundary value problems, DIFFERENCE equations, BOUNDARY value problems
Abstract

In this work, we consider nonlocal boundary value problems for parabolic equations on manifold. We set up the first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle. For the solutions of the difference scheme, we establish the stability estimates and coercivity estimates in various Hölder norms for the solutions of such boundary value problems. Furthermore, numerical results are given. [ABSTRACT FROM AUTHOR]

Published
2022
Full Text
View/download PDF

12. A note on parabolic differential equations on manifold.

Author

Ashyralyev, Allaberen, Sozen, Yasar, Hezenci, Fatih, Cakalli, Huseyin, Kocinac, Ljubisa D. R., Harte, Robin, Dik, Mehmet, Canak, Ibrahim, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, Onvural, Oruc Raif, and Sahin, Hakan

Subjects
*BOUNDARY value problems, *DIFFERENTIAL equations, *PARABOLIC differential equations, *COERCIVE fields (Electronics)
Abstract

The present extended abstract considers the differential equations on smooth closed manifolds, investigates and establishes the well-posedness of nonlocal boundary value problems (NBVP) in Hölder spaces. It also establishes new coercivity estimates in various Hölder norms for the solutions of such boundary value problems for parabolic equations. [ABSTRACT FROM AUTHOR]

Published
2020
Full Text
View/download PDF

13. A note on hyperbolic differential equations on manifold.

Author

Ashyralyev, Allaberen, Sozen, Yasar, Hezenci, Fatih, Ashralyyev, Charyyar, Erdogan, Abdullah S., Lukashov, Alexey, and Sadybekov, Makhmud

Subjects
*BOUNDARY value problems, *HYPERBOLIC functions, *HYPERBOLIC differential equations, *COERCIVE fields (Electronics), *EQUATIONS
Abstract

In this extended abstract, considering the differential equations on hyperbolic plane, we investigate and establish the well-posedness of boundary value problem for hyperbolic equations in Hölder spaces. Furthermore, we establish new coercivity estimates in various Hölder norms for the solutions of such boundary value problems for hyperbolic equations. [ABSTRACT FROM AUTHOR]

Published
2020
Full Text
View/download PDF

17. Reidemeister torsion of a symplectic complex

Author

Sozen, Yasar

Subjects
32G15, 57R30, Mathematics::Symplectic Geometry
Abstract

We consider a claim mentioned in [33] p.187 about the relation between a symplectic chain complex with $\omega$-compatible bases and Reidemeister Torsion of it. This is an explanation of it.

Published
2008

29. Reidemeister torsion of Hitchin representations of PSp2n(R).

Author

Sozen, Yasar

Subjects
*REIDEMEISTER torsion, *RIEMANN surfaces, *PIECEWISE linear topology, *MATHEMATICAL functions, *NUMERICAL analysis, *COEFFICIENTS (Statistics)
Abstract

We define Reidemeister torsion associated to a closed oriented Riemann surface Σ of genus at least 2 and with coefficients in the adjoint representation of Hitchin representations of PSp2n(R), n ≥ 1. Using symplectic chain complex, we present a volume element for Hitchin component of Hom (π1(Σ),PSp2n(R))/PSp2n(R) for n ≥ 1. [ABSTRACT FROM AUTHOR]

Published
2012
Full Text
View/download PDF

30. C-symplectic complex and Riedemeister torsion.

Author

Sozen, Yasar

Subjects
*SYMPLECTIC geometry, *TORSION theory (Algebra), *MATHEMATICAL formulas, *MANIFOLDS (Mathematics), *MATHEMATICAL analysis, *ALGEBRAIC functions
Abstract

In this article, we define C-symplectic chain complex. We also present a formula for the Reidemeister torsion of a C-symplectic chain complex. We apply the formula to closed manifolds. [ABSTRACT FROM AUTHOR]

Published
2012
Full Text
View/download PDF

31. Positivity of Two-Dimensional Elliptic Differential Operators with Nonlocal Conditions.

Author

Ashyralyev, Allaberen, Kaplan, Sema, and Sozen, Yasar

Subjects
DIFFERENTIAL operators, ELLIPTIC operators, POSITIVE operators, GREEN'S functions, BOUNDARY value problems, HOLDER spaces
Abstract

In the present paper, the differential operator A defined by ... with domain ... is considered. The Green function for A is constructed. The estimates for the Green function are obtained and the positivity of A in the Banach space C ([0,1] x R) is established. The structure of fractional spaces generated by A is investigated, the equivalence of the norm of these fractional spaces and Holder spaces is established. The positivity of A in the Holder space ... is obtained. [ABSTRACT FROM AUTHOR]

Published
2011
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results