Automorphisms of handlebodies arise naturally in the a classification of automorphisms of three-manifolds. Among automorphisms of handlebodies, there are certain automorphisms called irreducible (or generic), which are analogues of pseudo-Anosov automorphisms of surfaces. We show that irreducible automorphisms of handl…
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48 results for “Automorphisms”
Study shows RAAG automorphisms and outer automorphisms are not relatively hyperbolic.
problem Characterizing automorphism and outer automorphism groups of RAAGs.
method Analyzing groups of RAAGs with at least 3 vertices, categorizing based on graph structure.
result Automorphism and outer automorphism groups of RAAGs are not relatively hyperbolic.
Study knot invariants using automorphism groups of free nilpotent groups.
problem Developing knot invariants using automorphism groups.
method Nilpotently -localization of knot groups and automorphism groups of free nilpotent groups.
result Maps from outer automorphism groups yield knot invariants.
Constructs Cartan geometries from automorphism behaviors.
problem Determining Cartan geometries from automorphism local behavior.
method Introduces a construction for Cartan geometries capturing automorphism local behavior.
result The sprawl uniquely characterizes Cartan geometries with equivalent local behavior.
In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for , $\Aut(P_n)$ is generated by the subgroup $\Aut_c(P_n)$ of central automorphisms of , the subgroup $\Aut(B_n)$ of restrictions of automorphisms of on and one extra automorphism . W…
Automorphism groups of Hopf manifolds are finite and have a bounded order.
problem Understanding the structure of automorphism groups of Hopf manifolds.
method Proved that the automorphism groups of Hopf manifolds are Jordan.
result Automorphism groups of Hopf manifolds are finite and have a bounded order.
Automorphisms of pants complex are shown to be inner.
problem Understanding automorphisms of pants complexes.
method Proving automorphisms are inner for specific groups.
result Automorphism groups are naturally isomorphic to pants complex.
Classifies and constructs all extendable automorphisms of closed surfaces over the 3-sphere.
problem Identifying extendable automorphisms of closed surfaces over the 3-sphere.
method Classification and construction of extendable automorphisms through embeddings and Heegaard surfaces.
result All extendable automorphisms of closed surfaces can be induced by automorphisms of the 3-sphere on Heegaard surfaces.
Finite groups can be automorphism groups of translation surfaces with poles.
problem Existence of finite automorphism groups on translation surfaces with poles.
method Analyzing translation surfaces with poles and extending results to branched projective structures.
result Finite groups can be automorphism groups of translation surfaces with poles.
Automorphisms of Lie algebras and their root systems are fully lifted.
problem Understanding automorphisms of real semisimple Lie algebras and their root systems.
method Proving every automorphism of the restricted root system can be lifted to a Lie algebra automorphism.
result Automorphisms of restricted root systems can be fully lifted to Lie algebras.
Parabolic automorphisms on hyperkahler manifolds act ergodically on fibers.
problem Understanding the dynamics of parabolic automorphisms on hyperkahler manifolds.
method Analyzing the action of parabolic automorphisms on the second cohomology group and fibers of Lagrangian fibrations.
result Parabolic automorphisms preserving Lagrangian fibrations act ergodically on the fibers.
Proves strong Tits alternative for 3D automorphisms over zero char fields.
problem Tits alternative for 3D tame automorphisms over zero char fields.
method Proved strong Tits alternative using 3D tame automorphisms over zero char fields.
result Strong Tits alternative proven for 3D tame automorphisms over zero char fields.
Free groups' automorphisms have bounded orbits.
problem Understanding automorphisms of infinite rank free groups.
method Proved coarsely bounded automorphism groups via metric space actions.
result Free groups' automorphism groups have quasi-isometry type of a point.
Study growth rates of automorphisms of special groups.
problem Understanding the growth rates of automorphisms of special groups.
method Analyzing outer automorphisms of virtually special groups, showing polynomial or exponential growth, and constructing Nielsen-Thurston decompositions.
result Outer automorphism groups of virtually special groups are boundary amenable, have finite virtual cohomological dimension, and satisfy the Tits alternative.
Study on automorphisms of K3 and Enriques surfaces, proving entropy gaps and achirality.
problem Entropy norms and achirality of automorphisms on K3 and Enriques surfaces.
method Proves gap theorems for entropy norms and studies achirality in terms of genus-one fibrations.
result Entropy gaps and achirality results for automorphisms of K3 and Enriques surfaces.
Research examines octonionic slice regular functions and their automorphisms and invariants.
problem Analyzing slice regular functions in the octonionic algebra.
method Investigates automorphisms and invariants of octonionic slice regular functions.
result Characterizes the automorphisms and invariants of octonionic slice regular functions.
We consider automorphisms of homogeneous parabolic geometries with a fixed point. Parabolic geometries carry the distinguished distributions and we study those automorphisms which enjoy natural actions on the distributions at the fixed points. We describe the sets of such automorphisms on homogeneous parabolic geometri…
Study finds conditions for finite-dimensional Lie group structure in basic automorphism groups of certain Cartan foliations.
problem Characterizing the basic automorphism groups of Cartan foliations.
method Analyzes sufficient conditions and estimates dimensions for basic automorphism groups of Cartan foliations covered by fibrations.
result Identifies sufficient conditions for the existence of a finite-dimensional Lie group structure in basic automorphism groups.
Classifies hyperbolic manifolds with specific automorphism groups.
problem Classifying Kobayashi-hyperbolic manifolds with high-dimensional automorphism groups.
method Analyzes manifolds of dimension with automorphism groups of dimensions or .
result Completes the classification for automorphism groups and .
Paper describes invariants of slice regular functions' automorphism group.
problem Understanding invariants of slice regular functions' automorphism group.
method Analyzes automorphism group of slice regular functions over Clifford algebras.
result Describes invariants of the automorphism group of slice regular functions.
We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and Thurston, except an automorphism of a reducible manifold must first be written as…
We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a large automorphism group. We classify them when they are simply connected and the dimension of the automorphism group is maximal, and also prove a gap theorem for the dimension of the automorphism group.
Criterion for subgroup separability in outer automorphism groups.
problem Subgroup separability in outer automorphism groups.
method Criterion for separability of subgroups.
result Strengthening and generalizing a previous result on mapping class groups.
The study examines how automorphism growth rates of a group can be deduced from its simpler decompositions.
problem Determine automorphism growth rates of a group from its simpler decompositions.
method Analyze group decompositions into simpler pieces (direct products, free products, graph of groups) and deduce growth rates.
result Information about automorphism growth rates of a group can be deduced from its simpler decompositions.
Study automorphisms of smooth curve graphs on surfaces.
problem Understanding automorphisms of fine curve graphs.
method Examined automorphisms of continuously differentiable curves on surfaces.
result Automorphisms on surfaces of genus ≥ 2 are induced by homeomorphisms.
In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex with its additional structure the Torelli building of the surface in question. The…
CTs for free productsmath.GR
Outer automorphisms of free products are represented by CTs.
problem Representing outer automorphisms of free products by relative train track maps.
method Developed theory of attracting laminations and CTs for free products.
result Outer automorphisms of free products satisfy an index inequality.
Study shows pants graph automorphisms match mapping class groups of nonorientable surfaces.
problem Understanding automorphisms of pants graphs on nonorientable surfaces.
method Analyzing mapping class groups and proving isomorphism.
result Automorphism group of pants graphs isomorphic to mapping class groups.
Abstract Group Automorphisms of Two-Step Nilpotent Lie Groups and Partial Automatic Continuitymath.GR
The paper studies automorphisms of 2-step nilpotent Lie groups, showing continuity up to center and field automorphisms.
problem Investigating the continuity of abstract automorphisms in 2-step nilpotent Lie groups.
method Analyzes various types of 2-step nilpotent Lie groups, using tools from Riemannian geometry.
result Abstract automorphisms are continuous 'up to discontinuity due to the center and field automorphisms of ' for many 2-step nilpotent Lie groups.
The paper studies automorphisms of RAAGs and RACGs, proving properties of their fixed subgroups.
problem Fixed subgroups of automorphisms of RAAGs and RACGs.
method Introducing coarse-median preserving automorphisms and proving properties of fixed subgroups.
result Fixed subgroups of RAAGs and RACGs are finitely generated, undistorted, and quasi-convex.
Study automorphism groups of Inoue surfaces using quadratic number fields.
problem Understanding automorphism groups of Inoue surfaces.
method Construction and description of automorphism groups using quadratic number fields.
result Automorphism groups of Inoue surfaces described in terms of quadratic number fields.
Automorphisms of fine curve graph match surface homeomorphisms.
problem Understanding automorphisms of curve graphs for surfaces.
method Building on previous work, proving isomorphism to surface homeomorphisms.
result The group of automorphisms of the fine curve graph is isomorphic to the extended mapping class group of the surface.
We prove that the automorphism group of the dihedral quandle with n elements is isomorphic to the affine group of the integers mod n, and also obtain the inner automorphism group of this quandle. In [9], automorphism groups of quandles (up to isomorphisms) of order less than or equal to 5 were given. With the help of t…
We determine explicitly the structure of the automorphism group of a parabolic Inoue surface. We also describe the quotients of the surface by typical cyclic subgroups of the automorphism group.
Automorphisms of Kodaira surfaces are shown to be affine transformations.
problem Characterizing automorphisms of Kodaira surfaces.
method Analyzing lifts to the universal cover and conditions on affine transformations.
result Precise description of Kodaira surfaces' automorphism groups.
Study automorphism groups of quandles up to order 10.
problem Understanding automorphism groups of quandles of various orders.
method Enumerated and computed automorphism groups and displacement groups of quandles up to order 10.
result Computed automorphism groups and displacement groups for all quandles up to order 10.
Study on endomorphism and automorphism groups of specific quandles.
problem Characterizing endomorphism and automorphism groups of residually finite and profinite quandles.
method Proved properties of endomorphism monoids and automorphism groups for residually finite and profinite quandles.
result Endomorphism and automorphism groups of residually finite quandles are residually finite.
We find finite presentations for the automorphism group of the Artin pure braid group and the automorphism group of the pure braid group associated to the full monomial group.
We show that the automorphism group of the disk complex is isomorphic to the handlebody group. Using this, we prove that the outer automorphism group of the handlebody group is trivial.
Outer space and finiteness properties for symmetric automorphisms of RAAGs, and generalisationsmath.GR
Study on symmetric automorphisms of RAAGs, proving finiteness properties and contractibility.
problem Finiteness properties and contractibility of symmetric automorphisms of RAAGs.
method Definition of symmetric automorphism group, construction of symmetric Outer space, proof of contractibility.
result Finiteness properties and contractibility results for symmetric automorphisms of RAAGs.
Automorphisms of surfaces extendable over 4-sphere with invariant spin structures.
problem Extendability of automorphisms of surfaces over the 4-sphere.
method Constructing invariant spin structures and embeddings.
result Each automorphism of a surface is extendable over the 4-sphere after a connected sum with a torus.
Study automorphisms of pure braid groups on sphere homotopy groups.
problem Understanding automorphisms' effect on sphere homotopy groups.
method Examined Delta-group structure, proved invariance of cycle and boundary groups, computed action for few strands.
result Induced action of all automorphisms of pure braid groups on sphere homotopy groups.
It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal …
A completely nonintegrable -dimensional distribution on a -manifold is called an Engel structure. A -manifold with an Engel structure is called an Engel manifold. The developing map for an Engel manifold is very important tool to determine the Engel structure. Montgomery used it to prove that an Engel automorp…
Study shows automorphisms of Markov surfaces share periodic points if they share a common iterate.
problem Study of unlikely intersections for automorphisms of Markov surfaces with positive entropy.
method Arithmetic equidistribution for adelic line bundles, theory of laminar currents, quasi-Fuchsian representation theory.
result Two automorphisms with positive entropy share a Zariski dense set of periodic points if and only if they share a common iterate.
New proof shows smallest non-cyclic automorphism group quotients are linear 2-groups.
problem Identifying the smallest non-cyclic quotients of free group automorphism groups.
method Elementary proof using standard projection and automorphisms.
result All minimal quotients are linear groups over the field of two elements.
New criterion for bi-ordering free groups under automorphisms.
problem Bi-ordering free groups under automorphisms.
method New criterion for bi-ordering free groups.
result Fundamental group of the magic manifold is bi-orderable.
We give examples of endperiodic automorphisms.