scholarly journals Cohomology of $SL(2,C)$ Character Varieties of Surface Groups and the Action of the Torelli Group

2010 ◽  
Vol 14 (3) ◽  
pp. 359-384
Author(s):  
Georgios D. Daskalopoulos ◽  
Richard A. Wentworth ◽  
Graeme Wilkin
Keyword(s):  
Surface Groups ◽  
Torelli Group ◽  
Character Varieties

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 E-Polynomials of the SL(2, ℂ)-Character Varieties of Surface Groups

2015 ◽  
Vol 2016 (3) ◽  
pp. 926-961 ◽  
Author(s):  
Javier Martínez ◽  
Vicente Muñoz
Keyword(s):  
Surface Groups ◽  
Character Varieties

SL(2,?) character varieties of surface groups

2000 ◽  
Vol 101 (2) ◽  
pp. 189-207 ◽  
Author(s):  
R. Wentworth ◽  
S. Dostoglou ◽  
G. Daskalopoulos
Keyword(s):  
Surface Groups ◽  
Character Varieties

scholarly journals INTERSECTION COHOMOLOGY OF RANK 2 CHARACTER VARIETIES OF SURFACE GROUPS

2021 ◽  
pp. 1-40
Author(s):  
Mirko Mauri
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Compact Riemann Surface ◽  
Character Variety ◽  
Degree Zero ◽  
Surface Groups ◽  
Higgs Bundles ◽  
Character Varieties ◽  
Rank 2

Abstract For $G = \mathrm {GL}_2, \mathrm {SL}_2, \mathrm {PGL}_2$ we compute the intersection E-polynomials and the intersection Poincaré polynomials of the G-character variety of a compact Riemann surface C and of the moduli space of G-Higgs bundles on C of degree zero. We derive several results concerning the P=W conjectures for these singular moduli spaces.

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

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...

Sign in / Sign up

Export Citation Format

Share Document