scholarly journals Edge-preserving maps of the nonseparating curve graphs, curve graphs and rectangle preserving maps of the Hatcher–Thurston graphs

2020 ◽  
Vol 29 (11) ◽  
pp. 2050078
Author(s):  
Elmas Irmak
Keyword(s):  
Orientable Surface ◽  
Edge Preserving ◽  
Curve Graph ◽  
Genus Formula

Let [Formula: see text] be a compact, connected, orientable surface of genus [Formula: see text] with [Formula: see text] boundary components with [Formula: see text], [Formula: see text]. Let [Formula: see text] be the nonseparating curve graph, [Formula: see text] be the curve graph and [Formula: see text] be the Hatcher–Thurston graph of [Formula: see text]. We prove that if [Formula: see text] is an edge-preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We prove that if [Formula: see text] is an edge-preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We prove that if [Formula: see text] is closed and [Formula: see text] is a rectangle preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We also prove that these homeomorphisms are unique up to isotopy when [Formula: see text].

EXHAUSTION OF THE CURVE GRAPH VIA RIGID EXPANSIONS

2018 ◽  
Vol 61 (1) ◽  
pp. 195-230 ◽  
Author(s):  
JESÚS HERNÁNDEZ HERNÁNDEZ
Keyword(s):  
Topological Type ◽  
Orientable Surface ◽  
Finite Topological Type ◽  
Curve Graph ◽  
Finite Set ◽  
Rigid Set

AbstractFor an orientable surfaceSof finite topological type with genusg≥ 3, we construct a finite set of curves whose union of iterated rigid expansions is the curve graph$\mathcal{C}$(S). The set constructed, and the method of rigid expansion, are closely related to Aramayona and Leiniger's finite rigid set in Aramayona and Leininger,J. Topology Anal.5(2) (2013), 183–203 and Aramayona and Leininger,Pac. J. Math.282(2) (2016), 257–283, and in fact a consequence of our proof is that Aramayona and Leininger's set also exhausts the curve graph via rigid expansions.

Alternating maps on Hatcher–Thurston graphs

2017 ◽  
Vol 26 (11) ◽  
pp. 1750064 ◽  
Author(s):  
Jesús Hernández Hernández
Keyword(s):  
Edge Preserving ◽  
Genus Formula ◽  
Orientable Surfaces

Let [Formula: see text] and [Formula: see text] be connected orientable surfaces of genus [Formula: see text], [Formula: see text] punctures, and empty boundary. Let also [Formula: see text] be an edge-preserving alternating map between their Hatcher–Thurston graphs. We prove that [Formula: see text] and that there is also a multicurve of cardinality [Formula: see text] contained in every element of the image. We also prove that if [Formula: see text] and [Formula: see text], then the map [Formula: see text] obtained by filling the punctures of [Formula: see text], is induced by a homeomorphism of [Formula: see text].

scholarly journals Unicorn paths and hyperfiniteness for the mapping class group

2021 ◽  
Vol 9 ◽  
Author(s):  
Piotr Przytycki ◽  
Marcin Sabok
Keyword(s):  
Finite Type ◽  
Mapping Class Group ◽  
Class Group ◽  
Orientable Surface ◽  
Equivalence Relations ◽  
Mapping Class ◽  
Orbit Equivalence ◽  
Curve Graph

Abstract Let S be an orientable surface of finite type. Using Pho-on’s infinite unicorn paths, we prove the hyperfiniteness of orbit equivalence relations induced by the actions of the mapping class group of S on the Gromov boundaries of the arc graph and the curve graph of S. In the curve graph case, this strengthens the results of Hamenstädt and Kida that this action is universally amenable and that the mapping class group of S is exact.

scholarly journals Explicit solutions of certain orientable quadratic equations in free groups

2019 ◽  
Vol 29 (08) ◽  
pp. 1451-1466
Author(s):  
D. Gonçalves ◽  
T. Nasybullov
Keyword(s):  
Free Group ◽  
Homotopy Class ◽  
Explicit Solution ◽  
Orientable Surface ◽  
Explicit Solutions ◽  
Natural Homomorphism ◽  
Quadratic Equations ◽  
Wecken Property ◽  
Number Formula ◽  
Genus Formula

For [Formula: see text] denote by [Formula: see text] the free group on [Formula: see text] generators and let [Formula: see text]. For [Formula: see text] and elements [Formula: see text], we study orientable quadratic equations of the form [Formula: see text] with unknowns [Formula: see text] and provide explicit solutions for them for the minimal possible number [Formula: see text]. In the particular case when [Formula: see text], [Formula: see text] for [Formula: see text] and [Formula: see text] the minimal number which satisfies [Formula: see text], we provide two types of solutions depending on the image of the subgroup [Formula: see text] generated by the solution under the natural homomorphism [Formula: see text]: the first solution, which is called a primitive solution, satisfies [Formula: see text], the second solution satisfies [Formula: see text]. We also provide an explicit solution of the equation [Formula: see text] for [Formula: see text] in [Formula: see text], and prove that if [Formula: see text], then every solution of this equation is primitive. As a geometrical consequence, for every solution, we obtain a map [Formula: see text] from the orientable surface [Formula: see text] of genus [Formula: see text] to the torus [Formula: see text] which has the minimal number of roots among all maps from the homotopy class of [Formula: see text]. Depending on the number [Formula: see text], such maps have fundamentally different geometric properties: in some cases, they satisfy the Wecken property and in other cases not.

scholarly journals Geometric realizations of cyclic actions on surfaces

2019 ◽  
Vol 11 (04) ◽  
pp. 929-964
Author(s):  
Shiv Parsad ◽  
Kashyap Rajeevsarathy ◽  
Bidyut Sanki
Keyword(s):  
Finite Order ◽  
Representation Formula ◽  
Orientable Surface ◽  
Mapping Class ◽  
Realization Problem ◽  
Cyclic Subgroups ◽  
Genus Formula ◽  
Mapping Classes ◽  
Nielsen Realization ◽  
Maximal Reduction

Let [Formula: see text] denote the mapping class group of the closed orientable surface [Formula: see text] of genus [Formula: see text], and let [Formula: see text] be of finite order. We give an inductive procedure to construct an explicit hyperbolic structure on [Formula: see text] that realizes [Formula: see text] as an isometry. In other words, this procedure yields an explicit solution to the Nielsen realization problem for cyclic subgroups of [Formula: see text]. Furthermore, we give a purely combinatorial perspective by showing how certain finite order mapping classes can be viewed as fat graph automorphisms. As an application of our realizations, we determine the sizes of maximal reduction systems for certain finite order mapping classes. Moreover, we describe a method to compute the image of finite order mapping classes and the roots of Dehn twists, under the symplectic representation [Formula: see text].

Edge-Preserving Error Diffusion for Multi-Toning Based on Dual Quantization

2017 ◽  
Vol 2017 (18) ◽  
pp. 123-129
Author(s):  
Takuma Kiyotomo ◽  
Keisuke Hoshino ◽  
Yuki Tsukano ◽  
Hiroki Kibushi ◽  
Takahiko Horiuchi
Keyword(s):  
Error Diffusion ◽  
Edge Preserving

Material Identification in Presence of Metal for Baggage Screening

2020 ◽  
Vol 2020 (14) ◽  
pp. 294-1-294-8
Author(s):  
Sandamali Devadithya ◽  
David Castañón
Keyword(s):  
Atomic Number ◽  
Effective Atomic Number ◽  
Simulated Data ◽  
Dual Energy ◽  
Basis Functions ◽  
Total Variation Regularization ◽  
Ct Scanner ◽  
Edge Preserving ◽  
Baggage Screening ◽  
Dual Energy Imaging

Dual-energy imaging has emerged as a superior way to recognize materials in X-ray computed tomography. To estimate material properties such as effective atomic number and density, one often generates images in terms of basis functions. This requires decomposition of the dual-energy sinograms into basis sinograms, and subsequently reconstructing the basis images. However, the presence of metal can distort the reconstructed images. In this paper we investigate how photoelectric and Compton basis functions, and synthesized monochromatic basis (SMB) functions behave in the presence of metal and its effect on estimation of effective atomic number and density. Our results indicate that SMB functions, along with edge-preserving total variation regularization, show promise for improved material estimation in the presence of metal. The results are demonstrated using both simulated data as well as data collected from a dualenergy medical CT scanner.

Pre-Processing of Hyperspectral Images Using Nonlinear Filters

2013 ◽  
Vol 11 (1) ◽  
pp. 8-13
Author(s):  
V. Behar ◽  
V. Bogdanova
Keyword(s):  
Signal To Noise Ratio ◽  
Correlation Coefficients ◽  
Hyperspectral Images ◽  
Spectral Correlation ◽  
Edge Preserving ◽  
Improvement Factor ◽  
Filter Output ◽  
Average Improvement ◽  
Processing Procedure

Abstract In this paper the use of a set of nonlinear edge-preserving filters is proposed as a pre-processing stage with the purpose to improve the quality of hyperspectral images before object detection. The capability of each nonlinear filter to improve images, corrupted by spatially and spectrally correlated Gaussian noise, is evaluated in terms of the average Improvement factor in the Peak Signal to Noise Ratio (IPSNR), estimated at the filter output. The simulation results demonstrate that this pre-processing procedure is efficient only in case the spatial and spectral correlation coefficients of noise do not exceed the value of 0.6

New edge preserving enlargement algorithm for images

2013 ◽  
Vol 32 (11) ◽  
pp. 3182-3184
Author(s):  
Ye YUAN ◽  
Zhong-xu TIAN
Keyword(s):  
Edge Preserving
Sign in / Sign up

Export Citation Format

Share Document