arXiv research

Automorphisms of pants complex are shown to be inner.

Study shows pants graph automorphisms match mapping class groups of nonorientable surfaces.

Paper studies Engel structures and automorphisms on 4-manifolds.

Study automorphic and Lattès-type maps on manifolds, finding restrictions on their groups.

We show that the natural map from the mapping class groups of surfaces to the automorphism groups of free groups, induces an infinite loop map on the classifying spaces of the stable groups after plus construction. The proof uses automorphisms of free groups with boundaries which play the role of mapping class groups o…

We analyze the mapping class group of extendible automorphisms of the exterior boundary W of a compression body of dimension 3 or 4, which extend over the compression body (Q,V), where V is the interior boundary. Those that extend as automorphisms of (Q,V) rel V are called discrepant automorphisms, forming the mapping …

Isomorphic mapping class groups on infinite-type surfaces imply homeomorphic surfaces.

Study of infinite-type surfaces' automorphisms and graph structures.

Criterion for subgroup separability in outer automorphism groups.

Positive entropy automorphisms have virtual eigenvalues outside the unit circle.

Constructs pseudo-Anosov mappings related to toral automorphisms.

The study of which mapping class group elements can be realized as affine automorphisms of dilation surfaces.

The paper provides presentations for mapping class groups and cluster automorphism groups of surfaces.

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 …

Study of flip graphs and their automorphism groups for infinite-type surfaces.

Automorphisms of fine curve graph match surface homeomorphisms.

New technique shows any group can be a map's automorphism.

Automorphisms of free groups yield invariant posets of lamination orbits.

Finite automorphisms of SL(2,C) character varieties identified.

Let $G$ be the mapping torus of a polynomially growing automorphism of a finitely generated free group. We determine which epimorphisms from $G$ to $\mathbb{Z}$ have finitely generated kernel, and we compute the rank of the kernel. We thus describe all possible ways of expressing $G$ as the mapping torus of a free grou…

The thesis shows how automorphisms of hyperbolic groups can be represented by train track maps.

Study automorphisms on procongruence curve and pants complexes.

Automorphisms of surfaces extendable over 4-sphere with invariant spin structures.

The mapping class group of a Heegaard splitting is the group of automorphisms of the ambient 3-manifold that take the surface onto itself, modulo isotopies that keep the surface on itself. We characterize the mapping classes that restrict to periodic and reducible automorphisms of the surface.

Study knot invariants using automorphism groups of free nilpotent groups.

Outer automorphism group of hyperbolic groups is HHG under certain conditions.

The paper explores normal subgroups of braid groups and mapping class groups.

Every normal subgroup of Cantor tree's mapping class group is geometric.

Study reveals uniform difference in stretch factors between genus two handlebody group and outer automorphism group.

The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.

Paper disproves Wright's periodic map conjecture.

We define and discuss a notion called fibered commensurability of outer automorphisms of free groups. This notion lets us study symmetry of outer automorphisms. The notion of fibered commensurability is first defined by Calegari-Sun-Wang on mapping class groups. The Nielsen-Thurston type of mapping classes is a commens…

Proves normal subgroups of mapping class groups have specific properties.

Researchers prove the automorphism group of a sphere complex matches the mapping group of a graph.

Let Ng be the connected closed nonorientable surface of genus g >= 5 and Mod(Ng) denote the mapping class group of Ng. We prove that the outer automorphism group of Mod(Ng) is either trivial or Z if g is odd, and injects into the mapping class group of sphere with four holes if g is even.

Study on mapping classes of real rational surface automorphisms, focusing on reducible maps and pseudo-Anosov maps.

Study automorphism groups of Artin groups, proving rigidity and classification results.

Extremal metrics found on fibred Kähler manifolds with specific properties.

Outer automorphisms of free products are represented by CTs.

Maps between automorphism groups are isomorphisms for free factor complexes.

New maps on the plane with specific symmetry properties identified.

Many normal subgroups of mapping class groups are geometric.

The theorem connects surface mapping groups to fundamental groupoids.

We compute the rational stable homology of the automorphism groups of free nilpotent groups. These groups interpolate between the general linear groups over the ring of integers and the automorphism groups of free groups, and we employ functor homology to reduce to the abelian case. As an application, we also compute t…

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.

Study of Torelli subgroups of automorphism groups of free groups.

Introduces group-valued momentum maps for symplectic fiber bundles.

Recently there has been renewed interest in the mapping-class group of a compact surface of genus $g \ge 2$ and also in its finite order elements. A finite order element of the mapping-class group will be a conformal automorphisms on some Riemann surface of genus $g$. Here we give the details of the proof that there is…