New pseudomodular groups constructed from jigsaw construction.
problem Existence and properties of pseudomodular groups.
method Jigsaw construction of groups.
result Infinitely many simplest jigsaw groups are not pseudomodular.
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48 results for “group constructions”
Simple construction of Lie 2-groups from loop group extensions.
problem Constructing Lie 2-groups from loop group extensions.
method Using conjugation action of loop group on its central extension.
result Simple construction of string 2-group as a strict Fréchet Lie 2-group.
Riley "defined" the Heckoid groups for 2-bridge links as Kleinian groups, with nontrivial torsion, generated by two parabolic transformations, and he constructed an infinite family of epimorphisms from 2-bridge link groups onto Heckoid groups. In this paper, we make Riley's definition explicit, and give a systematic co…
Alternative construction of Rumin complex on Lie groups.
problem Constructing Rumin complex on homogeneous nilpotent Lie groups.
method Using ideas from parabolic geometry, an alternative construction to the classical one on Carnot groups.
result Explicit computations for the Engel group using the new approach.
Constructs Kleinian groups from free groups via hyperbolization.
problem Creating Kleinian groups from free groups.
method Direct product of rank 2 free groups and strict hyperbolization.
result Description of limit set and its topological dimension.
Extends Jones' construction to Thompson's group F and link homology.
problem Link homology and Thompson's group F.
method Asymptotic construction of -tangles in Thompson's group F.
result Asymptotically faithful association of -tangles with elements of Thompson's group F.
Paper uses Long-Moody construction for new braid group representations.
problem Constructing new representations of braid groups.
method Applies Fox derivation to matrix presentation of Long-Moody construction.
result Shows relation to twisted Alexander invariants.
We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used…
Geometrically constructs Virasoro-Bott group from circle diffeomorphisms.
problem Constructing the Virasoro-Bott group from circle diffeomorphisms.
method Analogous to loop group construction, using disc diffeomorphisms with special boundary conditions.
result Identifies Virasoro-Bott group as a quotient of disc diffeomorphisms with identified Lie algebra.
Uncountably many groups of type math.GR
We construct uncountably many discrete groups of type ; in particular we construct groups of type that do not embed in any finitely presented group. We compute the ordinary, - and compactly-supported cohomology of these groups. For each we construct a closed aspherical -manifold that admit…
In Part I of this series of papers, we made Riley's definition of Heckoid groups for 2-bridge links explicit, and gave a systematic construction of epimorphisms from 2-bridge link groups onto Heckoid groups, generalizing Riley's construction. In this paper, we give a complete characterization of upper-meridian-pair-pre…
New quasimorphisms constructed for manifolds with negative curvature.
problem Building quasimorphisms on manifolds with negative curvature.
method Generalizing Barge and Ghys construction to Lie groups.
result Counterexamples to Kapovich and Fujiwara theorem for Lie groups.
A cubical Rips constructionmath.GR
New group constructed from cube complex properties.
problem Creating a new group from cube complex properties.
method Cubical Rips construction for finitely presented groups.
result New group surjects onto a given group with specific properties.
New method constructs non-quasiconvex subgroups in hyperbolic groups.
problem Creating non-quasiconvex subgroups in hyperbolic groups.
method Using Stallings-like techniques on right-angled Coxeter groups (RACGs).
result Explicit examples of non-quasiconvex subgroups constructed.
We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Bar…
Sapir, Birget and Rips showed how to construct groups from Turing machines. To achieve such a construction they introduced the notion of S-machine. Then considering a simplified S-machine Sapir and Olshanskii showed how to construct a group such that each of its asymptotic cone is non-simply connected. Still using the …
The study constructs families of nilpotent Lie groups with geodesic orbit metrics.
problem Finding geodesic orbit metrics on nilpotent Lie groups.
method Construction of continuous families of nilpotent Lie groups.
result Continuous families of non-isomorphic nilpotent Lie groups with geodesic orbit metrics.
New method constructs multiple group racks, differing from known constructions.
problem Define new invariants for spatial surfaces.
method Using a G-family of racks and a normal subgroup N of G.
result New method yields multiple group racks not derived from known methods.
Constructs generalized Frobenius manifolds for specific Weyl groups.
problem Creating structures for orbit spaces of Weyl groups.
method Applying a previously established construction method to specific Weyl groups.
result Generalized Frobenius manifold structures constructed for and .
In this paper we construct the Differential calculus on the Hopf Group Coalgebra introduced by Turaev [10]. We proved that the concepts introduced by S.L.Woronowicz in constructing Differential calculus on Hopf Compact Matrix Pseudogroups (Quantum Groups)[7] can be adapted to serve again in our construction.
Paper connects algebraic and analytic methods for braid group representations.
problem Constructing representations of braid groups using algebraic and analytic approaches.
method Katz-Long-Moody construction and multiplicative middle convolution for KZ-type equations.
result Multiplicative middle convolution preserves unitarity and provides an algorithm to determine the signature of a Hermitian matrix.
Paper constructs hyperbolic Coxeter groups that virtually fiber over Z.
problem Creating hyperbolic Coxeter groups that virtually fiber.
method Iterative procedure combining Jankiewicz-Norin-Wise results and Osajda's construction.
result Proves construction of groups with increasing vcd with each iteration.
New subgroups of mapping class groups constructed for infinite-type surfaces.
problem Constructing new subgroups of mapping class groups for infinite-type surfaces.
method Utilization of special homeomorphisms called shift maps and multipush maps.
result Countably (and uncountably in certain cases) many non-conjugate embeddings of subgroups into mapping class groups.
We define a 3-loop group as a subgroup of smooth maps from a 3-ball to a Lie group , and then construct a 2-group based on an automorphic action on the Mickelsson-Faddeev extension of . In this we follow the strategy of Murray et al., who earlier described a similar construction in one dimension. The th…
A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscs.LG
New method constructs equivariant neural networks for arbitrary matrix groups.
problem Challenges in constructing equivariant neural networks for complex groups.
method Completely general algorithm for solving equivariant layers of matrix groups.
result Constructs multilayer perceptrons equivariant to multiple groups including O(1,3), O(5), Sp(n), and Rubik's cube group.
New groups constructed from tree automorphisms, proving finiteness.
problem Finiteness properties of self-similar and Röver groups.
method Braiding of self-similar groups, use of -ary cloning systems, analysis of embedded disks.
result Construction of a new group (braided Röver group) of type .
This paper explores links from Thompson's group conjugacy classes.
problem Understanding the relationship between Thompson's group conjugacy classes and links.
method Using Jones's construction to link elements of to unoriented links.
result Found sequences of elements from distinct conjugacy classes yielding specific links.
For every countable group G we construct a compact path connected subspace K of R^4 whose fundamental group is isomorphic to G. Our construction is much simpler than the one found recently by Virk.
Paper connects Stokes phenomena to quantum groups and Poisson-Lie groups.
problem Analyse Stokes phenomena in Poisson-Lie groups and quantum groups.
method Use Ug-valued Stokes phenomena to construct quantum group U_hg and relate it to Poisson-Lie group G*.
result Show that Ug-valued Stokes phenomena can be obtained as a semiclassical limit of the KZ associator.
We construct an embedding of any right-angled Artin group defined by a graph into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of . This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid g…
New method constructs explicit -harmonic functions on Lie groups.
problem Constructing proper -harmonic functions on Lie groups.
method Employing complex isoparametric functions to devise a general method.
result First explicit proper -harmonic functions on and .
The pants graph of a free group is constructed and studied.
problem Understanding the structure of free groups through graph theory.
method Developed a pants graph and studied its properties.
result The pants graph of a free group is connected and unbounded.
In this note we present a new construction of the string group that ends optionally in two different contexts: strict diffeological 2-groups or finite-dimensional Lie 2-groups. It is canonical in the sense that no choices are involved; all the data is written down and can be looked up (at least somewhere). The basis of…
The article constructs Fuchsian Schottky groups with conformal boundaries.
problem Creating generalized Schottky groups with specific properties.
method Developed Fuchsian Schottky groups by including orientation-reversing isometries.
result Decomposed compact core of conformally compact Riemann surfaces into pairs of pants.
The paper constructs infinite rank summands in diffeomorphism groups via Seiberg-Witten theory.
problem Constructing infinite rank summands in diffeomorphism groups.
method Using Seiberg-Witten theory, the paper constructs spherical families and computes invariants.
result Infinite rank summands in homotopy and homology groups of diffeomorphism groups.
Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.
problem Characterizing left-orderability in HNN extensions of groups.
method Analyzes HNN extensions of torsion-free nilpotent groups and left-orderable groups.
result Constructs examples of non-left-orderable HNN extensions of left-orderable groups.
Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a classical argument of Quillen, homological stability for the family of groups. We show that stability also holds with both polynomial…
We describe how an Ore category with a Garside family can be used to construct a classifying space for its fundamental group(s). The construction simultaneously generalizes Brady's classifying space for braid groups and the Stein--Farley complexes used for various relatives of Thompson's groups. It recovers the fact th…
We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh and involves mutations of quivers and diagrams defined in the theory of cluster algebras. We generalize our construction by assigning to every …
The study restricts groups in graph of groups structures.
problem Realizing groups as fundamental groups of graph of groups with restricted vertex groups.
method Analyzes restrictions on groups that can be realized and applies to manifold construction.
result Places constraints on groups that can be realized in graph of groups structures.
The Hessian geometry is the real analogue of the Kähler one. Sasakian geometry is an odd-dimensional counterpart of the Kähler geometry. In the paper, we study the connection between projective Hessian and Sasakian manifolds analogous to the one between Hessian and Kähler manifolds. In particular, we construct a Sasaki…
We construct quasi-isometric embeddings from right-angled Artin groups into the outer automorphism group of a free group. These homomorphisms are in analogy with those constructed in \cite{CLM}, where the target group is the mapping class group of a surface. Toward this goal, we develop tools in the free group setting …
In this paper we address the question of the existence of a model for the string 2-group as a strict Lie-2-group using the free loop group (or more generally for compact simple simply-connected Lie groups ). Baez-Crans-Stevenson-Schreiber constructed a model for the string 2-group using a based loop gro…
For every finitely generated abelian group G, we construct an irreducible open 3-manifold whose end set is homeomorphic to a Cantor set and with end homogeneity group of isomorphic to G. The end homogeneity group is the group of self-homeomorphisms of the end set that extend to homeomorphisms of the 3-m…
The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be used in a shear construction, which in algebraic form builds certain solvable Lie groups from Abelian ones. We discuss other examples of geo…
New method constructs proper affine actions of groups in higher dimensions.
problem Finding proper affine actions of discrete groups in higher-dimensional spaces.
method Higher strip deformations and Margulis invariant for properness.
result Affine actions of convex cocompact groups and virtually free groups are constructed properly.
Complete construction for Lie groups of types F4, E6, E7, E8.
problem Provide coordinates for surface representations into Lie groups of all types.
method Cluster ensemble framework, triangulated 3-manifolds, Fomin-Zelevinsky work.
result Complete construction for Lie groups of types F4, E6, E7, E8.
This paper is the second part of a two-part study of an elementary functorial construction of tesselated surfaces from finite groups. This elementary construction was discussed in the first part and generally results in a large collection of tesselated surfaces per group, for example when the construction is applied to…