SL(∞,ℝ), Higgs Bundles and Quantization

2018 ◽  
pp. 419-432
Author(s):  
Olivier Biquard
Keyword(s):  
Surface Groups ◽  
Higgs Bundles ◽  
Hitchin Component

Nigel Hitchin recently proposed a theory of SL(∞, R)-Higgs bundles which should parametrize a Hitchin component of representations of surface groups into SL(∞, R). This chapter discusses some properties and propose a formal approximation of SL(∞, R) representations by SL(n, R) representations in the large N limit, where n goes to infinity.

scholarly journals REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP

2011 ◽  
Vol 22 (02) ◽  
pp. 223-279 ◽  
Author(s):  
ANDRÉ GAMA OLIVEIRA
Keyword(s):  
Moduli Space ◽  
Riemann Surfaces ◽  
Connected Components ◽  
Higgs Bundles ◽  
Semisimple Lie Group ◽  
Projective Bundles ◽  
Compact Riemann Surfaces ◽  
Hitchin Component ◽  
Projective General Linear Group ◽  
Closed Oriented Surface

Given a closed, oriented surface X of genus g ≥ 2, and a semisimple Lie group G, let [Formula: see text] be the moduli space of reductive representations of π1X in G. We determine the number of connected components of [Formula: see text], for n ≥ 4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in [Formula: see text] is homotopically equivalent to [Formula: see text].

scholarly journals Asymptotics of Higgs bundles in the Hitchin component

2017 ◽  
Vol 307 ◽  
pp. 488-558 ◽  
Author(s):  
Brian Collier ◽  
Qiongling Li
Keyword(s):  
Higgs Bundles ◽  
Hitchin Component

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.

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.

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

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...

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