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.
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48 results for “complex automorphisms”
Automorphisms of contact graphs match those of cube complexes under weak conditions.
problem Understanding automorphisms of cube complexes and their contact graphs.
method Analyzing the relationship between automorphisms of cube complexes and their contact graphs.
result The automorphism groups of cube complexes and their contact graphs coincide under weak assumptions.
Outer automorphisms act loxodromically on a complex.
problem Understanding the dynamics of outer automorphisms on relative free factor complexes.
method Proving loxodromic action and north-south dynamics.
result Fully irreducible outer automorphisms act loxodromically on the relative free factor complex.
Study automorphism groups of Reeb components with complex leaves and solve functional equations.
problem Understanding the automorphism groups of Reeb components with complex structure.
method Review Hopf construction, solve Schröder's equation on the half line, analyze leafwise holomorphic automorphisms.
result Automorphism groups of Reeb components have infinite dimensions when leaf holonomy is trivial, finite dimensions otherwise.
Study automorphisms on procongruence curve and pants complexes.
problem Understanding automorphism groups of procongruence curve and pants complexes.
method Action on procongruence mapping class group and rigidity theorem for pants complex.
result Prove rigidity theorem for procongruence completion of pants complex.
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.
The study proves a theorem about subword complexity for free group automorphisms.
problem Analyzing subword complexity for attracting fixed points of automorphisms of free groups.
method Combinatorial arguments and train tracks.
result Subword complexity of attracting fixed points is equivalent to n, n log log n, n log n, or n^2.
In this paper, we study a flag complex which is naturally associated to the Thurston theory of surface diffeomorphisms for compact connected orientable surfaces with boundary. The various pieces of the Thurston decomposition of a surface diffeomorphism, thick domains and annular or thin domains, fit into this flag comp…
Complex of separating meridians can be extended to all meridians in genus ≥6 handlebodies.
problem Extending automorphisms of separating meridians to all meridians in handlebodies.
method Showing every automorphism of the complex of separating meridians can be extended to an automorphism on the complex of all meridians.
result Automorphisms of separating meridians can be extended to all meridians in handlebodies of genus ≥6.
Study leafwise holomorphic automorphisms of Reeb components.
problem Characterize automorphisms of Reeb components of leafwise complex foliations.
method Analyze Hopf construction and boundary holonomy properties.
result Determine structure of leafwise holomorphic automorphisms.
We show that there does not exist a Kobayashi hyperbolic complex manifold of dimension , whose group of holomorphic automorphisms has dimension and that, if a 3-dimensional connected hyperbolic complex manifold has automorphism group of dimension 10, then it is holomorphically equivalent to the Siegel s…
This paper classifies specific types of complex manifolds with high automorphism groups.
problem Classifying homogeneous Kobayashi-hyperbolic manifolds with high-dimensional automorphism groups.
method Analyzing manifolds of dimension and determining their automorphism groups.
result All connected homogeneous Kobayashi-hyperbolic manifolds of dimension are classified for specific automorphism group dimensions.
Study automorphisms of complex foliations in 3D.
problem Computing automorphisms of complex foliations in specific cases.
method Analyzing automorphisms of 3D Reeb components obtained by Hopf construction.
result Almost complete description of leafwise holomorphic automorphisms.
Study on automorphisms of complex -manifolds, extending previous work.
problem Investigate automorphisms of complex -manifolds with higher-order degeneracies.
method Extend Mendoza's definition of complex -manifolds to complex -manifolds and study their local and global automorphisms.
result Propose -analogues for classical spaces of holomorphic functions.
Conditions for hyperbolic and relatively hyperbolic extensions of free groups using automorphisms with fixed points.
problem Conditions for hyperbolic and relatively hyperbolic extensions of free groups.
method Using dynamics of outer automorphisms on the complex of free factors and investigating the geometry of the extension group.
result Conditions for hyperbolic and relatively hyperbolic extensions of free groups using automorphisms with fixed points.
Complex of cuts reveals full automorphism group for certain Stone spaces.
problem Understanding automorphism groups of Stone spaces.
method Introduced a complex of cuts and proved its significance.
result Full automorphism group identified for specific conditions.
Tree almost automorphism groups have a cellular action on a contractible complex.
problem Understanding the structure of tree almost automorphism groups.
method Showed cellular action on a contractible complex with specific stabilizers.
result Tree almost automorphism groups satisfy the -finiteness condition.
The paper studies Kobayashi pseudometric, complex automorphisms, and hyperkaehler manifolds.
problem Characterizing automorphisms and pseudodistances on complex manifolds.
method Defining Kobayashi quotient, proving isomorphisms, and analyzing pseudodistances.
result Proves Kobayashi's conjecture on hyperkaehler manifolds and automorphisms.
Characterizes groups arising as fixed subgroups of RAAG automorphisms.
problem Identifying groups that can be fixed by finite-order automorphisms of RAAGs.
method Geometric characterisation using divisible cube complexes.
result Surface groups and commutator subgroups of RAAGs are fixed subgroups.
No nontrivial automorphisms for cubic surfaces moduli space.
problem Understanding automorphisms of cubic surfaces moduli space.
method Analyzing the fundamental group of the moduli space.
result No nontrivial biholomorphic automorphisms for cubic surfaces moduli space.
Maps between automorphism groups are isomorphisms for free factor complexes.
problem Understanding the structure of automorphism groups of free factor complexes.
method Establishing isomorphisms between automorphism groups and automorphism groups of free factor complexes.
result Natural maps from to the automorphism group of the free-factor complex are isomorphisms.
Classifies complex structures on SL(2,C), finding new non-regular ones.
problem Classifying complex structures on SL(2,C) up to automorphisms.
method Classification via Lie group automorphisms and topological analysis.
result Found one new, non-regular complex structure.
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…
We show that the automorphism group of the complex of pants decompositions for a surface is isomorphic to the mapping class group for that surface.
Groups of birational transformations with specific properties are conjugate to groups of pseudo-automorphisms.
problem Classifying groups of birational transformations with fixed point properties.
method Importing ideas from geometric group theory, proving conjugacy to groups of pseudo-automorphisms.
result Groups of birational transformations with certain properties are conjugate to groups of pseudo-automorphisms.
On the automorphism group of the asymptotic pants complex of a planar surface of infinite typemath.GN
We consider a planar surface Σof infinite type which has the Thompson group T as asymptotic mapping class group. We construct the asymptotic pants complex C of Σand prove that the group T acts transitively by automorphisms on it. Finally, we establish that the automorphism group of the complex C is an extension of the …
Acylindrical hyperbolicity proven for a specific group of automorphisms.
problem Proving the acylindrical hyperbolicity of a group of automorphisms.
method Study of a 2D simplicial complex and proving its contractibility and Gromov-hyperbolicity; finding loxodromic elements.
result Tame automorphism group is acylindrically hyperbolic.
Unipotent automorphisms on complex supermanifolds are studied for classification.
problem Classifying supermanifolds based on unipotent automorphisms.
method Analyzing even global degree increasing vector fields and their kernels.
result Classification of strictly -nildominated supermanifolds up to degree .
Positive entropy automorphisms have virtual eigenvalues outside the unit circle.
problem Understanding the dynamics of surface automorphisms with positive entropy.
method Investigating virtual homological eigenvalues of surface automorphisms.
result Existence of virtual eigenvalues outside the unit circle for automorphisms with positive entropy.
New proof for quaternionic structures on specific manifolds via automorphisms.
problem Characterizing quaternionic triple integrable complex structures on group manifolds and homogeneous spaces.
method Using automorphisms of the Lie algebra to construct quaternion triples.
result Simplified construction of quaternion triples on specific manifolds.
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.
Study automorphisms and real structures on a special super-Grassmannian.
problem Investigate automorphisms and real structures on a -symmetric super-Grassmannian.
method Investigate automorphisms and real structures on a -symmetric super-Grassmannian using Galois cohomology.
result Classify real structures on and compute corresponding supermanifolds of real points.
Study shows top homology group isn't dualizing module for automorphism group of free groups.
problem Identifying the dualizing module for automorphism group of free groups.
method Analyzing the top homology group of the free factor complex.
result The top homology group is not the dualizing module for , especially for .
Isomorphic mapping class groups on infinite-type surfaces imply homeomorphic surfaces.
problem Characterizing isomorphisms between mapping class groups of infinite-type surfaces.
method Proving that all simplicial automorphisms are induced by homeomorphisms and applying to mapping class groups.
result Isomorphic big mapping class groups imply homeomorphic underlying surfaces.
This goal of the paper is to show that the automorphisms of the complex of curves in a surface are induced by the self-homeomorphisms of the surface except the surface is the 2-holed torus.
Maximal automorphisms found for complex projective structures.
problem Maximizing automorphisms in complex projective structures.
method Analyzing Fuchsian uniformizations and Galois Belyi curves.
result Fuchsian uniformizations of Hurwitz surfaces achieve maximal automorphisms.
We compute the automorphism groups of the Torelli complex and the complex of separating curves for all but finitely many compact orientable surfaces. As an application, we show that the abstract commensurators of the Torelli group and the Johnson kernel for such surfaces are naturally isomorphic to the extended mapping…
In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the automorphism group and the regularity of the boundary.
The main goal of this paper is a calculation of the integral (co)homology of the group of symmetric automorphisms of a free product. We proceed by giving a geometric interpretation of symmetric automorphisms via a moduli space of certain diagrams, which we name cactus products. To describe this moduli space a theory of…
A connected Fano complex-contact manifold is isomorphic to the kaehlerian C-space of Boothby type with a natural complex-contact structure corresponding to a non-abelian simple complex Lie algebra if the contact line bundle is very ample. A. Beauville relaxed the provision to two assumptions that the contact line bundl…
Study shows infinite manifold types for every group.
problem Finding manifold types for every finite group.
method Proved existence of infinitely many compact complex hyperbolic 2-manifolds.
result For every finite group, there are infinitely many isomorphism classes of compact complex hyperbolic 2-manifolds with automorphism group isomorphic to the group.
Approximates symplectic automorphisms of coadjoint orbits using Hamiltonian Carleman methods.
problem Approximating symplectic automorphisms of coadjoint orbits.
method Hamiltonian Carleman approximation for coadjoint orbits of complex Lie groups.
result Established the Hamiltonian density property for closed coadjoint orbits of all complex Lie groups.
Researchers prove the automorphism group of a sphere complex matches the mapping group of a graph.
problem Understanding the automorphisms of sphere complexes associated with graphs.
method Analyzing the group of proper homotopy equivalences and constructing an exhaustion of the sphere complex.
result The automorphism group of the sphere complex is isomorphic to the mapping group of the graph.
The curve complex of a 3-holed projective plane is shown to be quasi-isometric to a tree and its automorphisms are isomorphic to the mapping class group.
problem Characterizing the automorphisms of the curve complex of a 3-holed projective plane.
method Exhaustion of the curve complex by finite rigid sets, quasi-isometry to a tree, and isomorphism to the mapping class group.
result The group of simplicial automorphisms of the curve complex is isomorphic to the mapping class group.
Criteria for lifting manifold diffeomorphisms to vector bundle automorphisms.
problem Lifting diffeomorphisms to vector bundles.
method Criteria for lifting diffeomorphisms to linear automorphisms of vector bundles.
result Criteria for lifting diffeomorphisms to linear automorphisms of vector bundles.
In this paper we determine all Kobayashi-hyperbolic 2-dimensional complex manifolds for which the group of holomorphic automorphisms has dimension 3. This work concludes a recent series of papers by the author on the classification of hyperbolic -dimensional manifolds, with automorphism group of dimension at least $…
Let be a connected nonorientable surface of genus with punctures. Suppose that is odd and . We prove that the automorphism group of the complex of curves of is isomorphic to the mapping class group of .
Almost complex structures in 6D with nondegenerate Nijenhuis tensors and large symmetry groupsmath.DG
The paper explores 6D almost complex structures with maximal symmetry groups.
problem Finding the largest automorphism groups of 6D almost complex structures.
method Analyzing the Nijenhuis tensor and automorphism groups of 6D almost complex structures.
result The largest automorphism group dimension is 10, realized by 3 strictly nearly Kähler spaces.