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 VIRTUAL ALGEBRAIC FIBRATIONS OF KÄHLER GROUPS

2019 ◽  
pp. 1-19
Author(s):  
STEFAN FRIEDL ◽  
STEFANO VIDUSSI
Keyword(s):  
Fundamental Group ◽  
Finite Index ◽  
Surface Groups ◽  
Index Subgroup ◽  
Finitely Generated ◽  
Kähler Surfaces ◽  
Kähler Groups ◽  
Strong Relation ◽  
Finite Index Subgroup ◽  
Finite Index Subgroups

This paper stems from the observation (arising from work of Delzant) that “most” Kähler groups $G$ virtually algebraically fiber, that is, admit a finite index subgroup that maps onto $\mathbb{Z}$ with finitely generated kernel. For the remaining ones, the Albanese dimension of all finite index subgroups is at most one, that is, they have virtual Albanese dimension $va(G)\leqslant 1$ . We show that the existence of algebraic fibrations has implications in the study of coherence and higher BNSR invariants of the fundamental group of aspherical Kähler surfaces. The class of Kähler groups with $va(G)=1$ includes virtual surface groups. Further examples exist; nonetheless, they exhibit a strong relation with surface groups. In fact, we show that the Green–Lazarsfeld sets of groups with $va(G)=1$ (virtually) coincide with those of surface groups, and furthermore that the only virtually RFRS groups with $va(G)=1$ are virtually surface groups.

Subgroups of products of surface groups

1999 ◽  
Vol 126 (2) ◽  
pp. 195-208 ◽  
Author(s):  
F. E. A. JOHNSON
Keyword(s):  
Direct Product ◽  
Free Groups ◽  
Orientable Surface ◽  
Fuchsian Groups ◽  
Surface Groups ◽  
Finitely Generated ◽  
Isomorphism Classes ◽  
Relative Invariant ◽  
Finiteness Result ◽  
Subdirect Products

The subgroup structure of a direct product of two Fuchsian groups is very complicated; for example, Baumslag and Roseblade [1] have shown that a direct product Fm1×Fm2 of finitely generated free groups contains continuously many distinct isomorphism classes of finitely generated subgroups. The situation is much simpler, however, if attention is restricted to finitely generated normal subgroups of Fm1×Fm2; then on general grounds one cannot expect to get more than a countable infinity, but, in fact, the situation is almost finite; we showed, in [4], that Fm1×Fm2 contains precisely 1+min{m1, m2} orbits of maximal normal subdirect products under the natural action of its automorphism group.In this paper we study the situation which arises if the free groups Fmi are replaced by fundamental groups of closed surfaces. This question was previously considered by Nigel Carr in the final chapter of his (unpublished) thesis [2]. By appealing to the relative invariant theory of pairs of skew bilinear forms, Carr was able to show that in a direct product Σg1×Σg2 of orientable surface groups of genus [ges ]2 the number of orbits of maximal normal subdirect products is always infinite. Here we refine and extend Carr's approach to study the manner in which the finiteness result of [4] breaks down on passing to more general Fuchsian groups.

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 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 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 On the lattice of varieties of completely regular semigroups

1983 ◽  
Vol 35 (2) ◽  
pp. 227-235 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Lattice Of Varieties ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Variety Of Groups ◽  
Completely Regular Semigroups ◽  
Subdirect Products

AbstractSeveral morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

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