Invariant weakly convex cocompact subspaces for surface groups in $A_2$-buildings

2021 ◽  
pp. 1
Author(s):  
Anne Parreau
Keyword(s):  
Surface Groups ◽  
Weakly Convex ◽  
Convex Cocompact

scholarly journals Surface groups acting on spaces

2017 ◽  
Vol 39 (7) ◽  
pp. 1843-1856
Author(s):  
GEORGIOS DASKALOPOULOS ◽  
CHIKAKO MESE ◽  
ANDREW SANDERS ◽  
ALINA VDOVINA
Keyword(s):  
Hausdorff Dimension ◽  
Group Action ◽  
Metric Space ◽  
Hyperbolic Plane ◽  
Harmonic Map ◽  
Surface Group ◽  
Surface Groups ◽  
Limit Set ◽  
Convex Cocompact

Harmonic map theory is used to show that a convex cocompact surface group action on a $\text{CAT}(-1)$ metric space fixes a convex copy of the hyperbolic plane (i.e. the action is Fuchsian) if and only if the Hausdorff dimension of the limit set of the action is equal to 1. This provides another proof of a result of Bonk and Kleiner. More generally, we show that the limit set of every convex cocompact surface group action on a $\text{CAT}(-1)$ space has Hausdorff dimension $\geq 1$, where the inequality is strict unless the action is Fuchsian.

Reactive Nanopattern in a Triple Structured Bio-Inspired Honeycomb Film as a Clickable Platform

2018 ◽  
Author(s):  
Pierre Marcasuzaa ◽  
Samuel Pearson ◽  
Karell Bosson ◽  
Laurence Pessoni ◽  
Jean-Charles Dupin ◽  
...  
Keyword(s):  
Self Assembly ◽  
Double Porosity ◽  
Surface Groups ◽  
Specific Chemical ◽  
Site Specific ◽  
Surface Functionality ◽  
Wenzel State ◽  
Breath Figure ◽  
Responsive Surfaces ◽  
Secondary Population

A hierarchically structured platform was obtained from spontaneous self-assembly of a poly(styrene)-<i>b</i>-poly(vinylbenzylchloride) (PS-<i>b</i>-PVBC) block copolymer (BCP) during breath figure (BF) templating. The BF process using a water/ethanol atmosphere gave a unique double porosity in which hexagonally arranged micron-sized pores were encircled by a secondary population of smaller, nano-sized pores. A third level of structuration was simultaneously introduced between the pores by directed BCP self-assembly to form out-of-the-plane nano-cylinders, offering very rapid bottom-up access to a film with unprecedented triple structure which could be used as a reactive platform for introducing further surface functionality. The surface nano-domains of VBC were exploited as reactive nano-patterns for site-specific chemical functionalization by firstly substituting the exposed chlorine moiety with azide, then “clicking” an alkyne by copper (I) catalyzed azide-alkyne Huisgen cycloaddition (CuAAC). Successful chemical modification was verified by NMR spectroscopy, FTIR spectroscopy, and XPS, with retention of the micro- and nanostructuration confirmed by SEM and AFM respectively. Protonation of the cyclotriazole surface groups triggered a switch in macroscopic behavior from a Cassie-Baxter state to a Wenzel state, highlighting the possibility of producing responsive surfaces with hierarchical structure.

scholarly journals Kähler groups and subdirect products of surface groups

2020 ◽  
Vol 24 (2) ◽  
pp. 971-1017
Author(s):  
Claudio Llosa Isenrich
Keyword(s):  
Surface Groups ◽  
Kähler Groups ◽  
Subdirect Products

scholarly journals Solid-phase extraction cartridges with multi-walled carbon nanotubes and effect of the oxygen functionalities on the recovery efficiency of organic micropollutants

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Marta O. Barbosa ◽  
Rui S. Ribeiro ◽  
Ana R. L. Ribeiro ◽  
M. Fernando R. Pereira ◽  
Adrián M. T. Silva
Keyword(s):  
Carbon Nanotubes ◽  
Solid Phase Extraction ◽  
Solid Phase ◽  
Surface Groups ◽  
Phase Extraction ◽  
Organic Micropollutants ◽  
Oxidation Method ◽  
Hydrothermal Oxidation ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

AbstractPristine and functionalized multi-walled carbon nanotubes (MWCNTs) were investigated as adsorbent materials inside solid-phase extraction (SPE) cartridges for extraction and preconcentration of 8 EU-relevant organic micropollutants (with different pKa and polarity) before chromatographic analysis of surface water. The recoveries obtained were > 60% for 5/8 target pollutants (acetamiprid, atrazine, carbamazepine, diclofenac, and isoproturon) using a low amount of this reusable adsorbent (50 mg) and an eco-friendly solvent (ethanol) for both conditioning and elution steps. The introduction of oxygenated surface groups in the carbon nanotubes by using a controlled HNO3 hydrothermal oxidation method, considerably improved the recoveries obtained for PFOS (perfluorooctanesulfonic acid) and methiocarb, which was ascribed to the hydrogen bond adsorption mechanism, but decreased those observed for the pesticide acetamiprid and for two pharmaceuticals (carbamazepine and diclofenac), suggesting π–π dispersive interactions. Moreover, a good correlation was found between the recovery obtained for methiocarb and the amount of oxygenated surface groups on functionalized MWCNTs, which was mainly attributed to the increase of phenols and carbonyl and quinone groups. Thus, the HNO3 hydrothermal oxidation method can be used to finely tune the surface chemistry (and texture) of MWCNTs according to the specific micropollutants to be extracted and quantified in real water samples.

Hierarchical Crumpled NiMn2O4@MXene Composites for High Rate Ion Transport Electrochemical Supercapacitors

2021 ◽  
Author(s):  
Hailong Yan ◽  
Jinbing Cheng ◽  
Zuxue Bai ◽  
Tao Peng ◽  
Jang-Kyo Kim ◽  
...  
Keyword(s):  
Ion Transport ◽  
Electronic Conductivity ◽  
High Rate ◽  
Surface Groups ◽  
Hydrophilic Surface ◽  
Electrochemical Supercapacitors ◽  
Excellent Performance ◽  
Volumetric Capacitance

MXenes have received great attention due to their excellent performance such as metal-like electronic conductivity, hydrophilic surface groups, and high volumetric capacitance. However, many performances of MXenes are still unsatisfied...

scholarly journals The local-to-global property for Morse quasi-geodesics

2021 ◽  
Author(s):  
Jacob Russell ◽  
Davide Spriano ◽  
Hung Cong Tran
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Type Theorem ◽  
Hyperbolic Groups ◽  
Global Property ◽  
Mapping Class ◽  
Relatively Hyperbolic Groups ◽  
Convex Cocompact ◽  
Relatively Hyperbolic ◽  
Translation Length

AbstractWe show the mapping class group, $${{\,\mathrm{CAT}\,}}(0)$$ CAT ( 0 ) groups, the fundamental groups of closed 3-manifolds, and certain relatively hyperbolic groups have a local-to-global property for Morse quasi-geodesics. This allows us to generalize combination theorems of Gitik for quasiconvex subgroups of hyperbolic groups to the stable subgroups of these groups. In the case of the mapping class group, this gives combination theorems for convex cocompact subgroups. We show a number of additional consequences of this local-to-global property, including a Cartan–Hadamard type theorem for detecting hyperbolicity locally and discreteness of translation length of conjugacy classes of Morse elements with a fixed gauge. To prove the relatively hyperbolic case, we develop a theory of deep points for local quasi-geodesics in relatively hyperbolic spaces, extending work of Hruska.

scholarly journals Topological mirror symmetry for rank two character varieties of surface groups

2021 ◽  
Author(s):  
Mirko Mauri
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Surface Groups ◽  
Character Varieties ◽  
Hitchin System ◽  
Global Topology ◽  
Hodge Numbers

AbstractThe moduli spaces of flat $${\text{SL}}_2$$ SL 2 - and $${\text{PGL}}_2$$ PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.

scholarly journals Geodesic planes in geometrically finite acylindrical -manifolds

2021 ◽  
pp. 1-40
Author(s):  
YVES BENOIST ◽  
HEE OH
Keyword(s):  
Closed Geodesic ◽  
Duke Math ◽  
Geometrically Finite ◽  
Convex Cocompact ◽  
Invent Math ◽  
Convex Core

Abstract Let M be a geometrically finite acylindrical hyperbolic $3$ -manifold and let $M^*$ denote the interior of the convex core of M. We show that any geodesic plane in $M^*$ is either closed or dense, and that there are only countably many closed geodesic planes in $M^*$ . These results were obtained by McMullen, Mohammadi and Oh [Geodesic planes in hyperbolic 3-manifolds. Invent. Math.209 (2017), 425–461; Geodesic planes in the convex core of an acylindrical 3-manifold. Duke Math. J., to appear, Preprint, 2018, arXiv:1802.03853] when M is convex cocompact. As a corollary, we obtain that when M covers an arithmetic hyperbolic $3$ -manifold $M_0$ , the topological behavior of a geodesic plane in $M^*$ is governed by that of the corresponding plane in $M_0$ . We construct a counterexample of this phenomenon when $M_0$ is non-arithmetic.

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