A5039561215- Geometric and Algebraic Topology
- Homotopy and Cohomology in Algebraic Topology
- Mathematical Dynamics and Fractals
- semigroups and automata theory
- Finite Group Theory Research
- Advanced Operator Algebra Research
- Topological and Geometric Data Analysis
- Advanced Combinatorial Mathematics
- Advanced Topology and Set Theory
- Algebraic Geometry and Number Theory
- Advanced Algebra and Geometry
- Rings, Modules, and Algebras
- Mathematics and Applications
- Computability, Logic, AI Algorithms
- graph theory and CDMA systems
- Geometry and complex manifolds
- Geometric Analysis and Curvature Flows
- Computational Geometry and Mesh Generation
- Limits and Structures in Graph Theory
- Dental Research and COVID-19
- Advanced Graph Theory Research
- CRISPR and Genetic Engineering
- SARS-CoV-2 detection and testing
- SARS-CoV-2 and COVID-19 Research
- Cellular Automata and Applications
McGill University
2015-2024
University of Cambridge
2020-2022
New York University
2022
University of Richmond
2022
AstraZeneca (United Kingdom)
2021
AstraZeneca (Brazil)
2021
Royal Liverpool University Hospital
2020
University of Liverpool
2020
University of Michigan
2016
Technion – Israel Institute of Technology
2015
We give a criterion in terms of the boundary for existence proper cocompact action word-hyperbolic group on ${\rm CAT}(0)$ cube complex. describe applications towards lattices and hyperbolic 3-manifold groups. In particular, by combining theory special complexes, surface subgroup result Kahn-Markovic, Agol's criterion, we find that every separable closed is virtually fibered.
Let $G$ be a word-hyperbolic group with quasiconvex hierarchy.We show that has finite index subgroup $G'$ embeds as of right-angled Artin group.It follows every is virtual retract,and hence separable.The results are applied to certain 3-manifold and one-relator groups.
We prove that the fundamental groups of 'standard' arithmetic hyperbolic manifolds virtually retract onto their geometrically finite subgroups. In particular, this implies homology immersed totally geodesic hypersurfaces compact inject in ambient manifold.
Abstract We give a generalized and self-contained account of Haglund–Paulin’s wallspaces Sageev’s construction the CAT(0) cube complex dual to wallspace. examine criteria on wallspace leading finiteness properties its complex. Our discussion is aimed at readers wishing apply these methods produce actions groups complexes understand their nature. develop ideas in level generality that facilitates application. main result describes structure arising from relatively hyperbolic groups. Let...
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a compact oriented irreducible alttext="3"> <mml:mn>3</mml:mn> encoding="application/x-tex">3</mml:annotation> </inline-formula>-manifold which is neither graph manifold nor hyperbolic manifold. We prove that alttext="pi 1...
Significance Genetically modified animals are crucial for functional studies and translational biomedical research. However, the generation of genome-edited large is time consuming inefficient. Here, we report transgenic pigs chickens that ubiquitously express Cas9 nuclease. The functionality was demonstrated different target genes, a variety cell types, in vivo heart developing brain. Genome editing can now easily be carried out specific organs or tissues without need to generate...
Graph groups are with presentations where the only relators commutators of generators. were first investigated by Baudisch [1], and much subsequent foundational work was done Droms, B. Servatius, H. Servatius [3; 4; 5]. Later, more general construction graph products (Definition 2.1) introduced developed Green [7]. (Graph to free as groups.) have also been recent interest because their geometric properties (Hermiller Meier [8] VanWyk [13]) cohomological subgroups (Bestvina Brady [2]). In...
We introduce the bounded packing property for a subgroup of countable discrete group G. This gives finite upper bound on number left cosets that are pairwise close in establish basic properties packing, and give many examples; instance, every countable, virtually nilpotent has packing. explain several natural connections between actions CAT(0) cube complexes. Our main result establishes relatively quasiconvex subgroups hyperbolic group, under mild hypotheses. As an application, we prove have...
We prove that random groups at density less than $\frac 16$ act freely and cocompactly on CAT(0) cube complexes, 15$ have codimension-$1$ subgroups. In particular, Property $(T)$ fails to hold 15$. Abstract. Nous prouvons que les groupes aléatoires en densité strictement inférieure à agissent librement et cocompactement sur un complexe cubique CAT(0). De plus 15$, ils ont sous-groupe de codimension $1$; particulier, la propriété n'est pas vérifiée.
We prove that certain compact cube complexes have special finite covers.This means they covers whose fundamental groups are quasiconvex subgroups of right-angled Artin groups.As a result we obtain linearity and the separability for consider.Our applies, in particular, to negatively curved complex hyperplanes do not self-intersect.For with word-hyperbolic group, show it is virtually if only its hyperplane stabilizers separable.In final application, every simple type uniform arithmetic...
Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in are separable π1M, and the double cosets for crossing also separable. deduce if there is 'sufficient' collection M, then π1M virtually group special non-positively curved cube complex. provide sufficient manifolds with boundary, thus proving their special, hence linear.
A Tits alternative theorem is proved in this paper for groups acting on CAT(0) cubical complexes. That is, a proof given to show that if G assumed be group which there bound the orders of its finite subgroups, and acts properly finite-dimensional complex, then either contains free subgroup rank 2, or finitely generated virtually abelian. In particular, above conclusion holds any with action complex. 2000 Mathematics Subject Classification 20F67, 20E08.
This paper provides a strengthening of the theorems small cancellation theory. It is proven that disc diagrams contain 'fans' consecutive 2-cells along their boundaries. The size these fans linked to strength conditions satisfied by diagram. A classification result for satisfying conditions. Any diagram either contains three its boundary, or it ladder, wheel. Similar statements are annular diagrams. 2000 Mathematical Subject Classification: 20F06.
It is shown that π1 of a finite graph free groups with cyclic edge subgroup separable unless has non-trivial element g such gn ∼ gm n ≠ ±m. easy to decide from the presentation if conjugacy exists.
We explore the combination theorem for a group G splitting as graph of relatively hyperbolic groups. Using fine approach to relative hyperbolicity, we find short proofs hyperbolicity under certain conditions. then provide criterion quasiconvexity subgroup H depending on intersection with vertex groups G. give an application towards local quasiconvexity.
We prove that if S is a properly embedded incompressible surface in compact 3-manifold M, then the fundamental group of separable M.