arXiv research

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.

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

Proves Farrell--Jones Conjecture for hyperbolic groups and their automorphisms.

The paper studies automorphisms of 2-step nilpotent Lie groups, showing continuity up to center and field automorphisms.

Minimal surfaces with negative curvature found in large spheres.

Classifies 3D manifolds with specific structures and automorphisms.

The paper extends arithmetic quotient results to right-angled Artin groups.

We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various nilpotent quotients. We show that much like the structure of a nilpotent group is dictated to a large degree by its abelianization,…

Compact Lie groups can be realized as automorphism groups of Riemannian manifolds.

Study of automorphisms and splittings of special groups, showing infinite groups under certain conditions.

For a fully irreducible automorphism φof the free group F_k we compute the asymptotics of the intersection number n \mapsto i(T,T'φ^n) for trees T,T' in Outer space. We also obtain qualitative information about the geometry of the Guirardel core for the trees T and T'φ^n for n large.

The study examines power quotients of surface groups and mapping class groups, proving structural properties and isomorphisms.

The study examines the rigidity of mapping class groups under large powers of twists.

The paper constructs contact-hyperbolic manifolds with large automorphism groups.

Study knot invariants using automorphism groups of free nilpotent groups.

Study shows RAAG automorphisms and outer automorphisms are not relatively hyperbolic.

The study proves fixed-point theorems for groups acting on CAT(0) spaces.

Free groups' automorphisms have bounded orbits.

Finite groups can be automorphism groups of translation surfaces with poles.

Automorphisms of pants complex are shown to be inner.

Study finite group actions on aspherical manifolds, proving rigidity and symmetry bounds.

Study finds conditions for finite-dimensional Lie group structure in basic automorphism groups of certain Cartan foliations.

Automorphism groups of Hopf manifolds are finite and have a bounded order.

Study of Dehn twists in free groups generates right-angled Artin groups.

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.

Criterion for subgroup separability in outer automorphism groups.

Study growth rates of automorphisms of special groups.

Study automorphisms of pure braid groups on sphere homotopy groups.

New proof shows smallest non-cyclic automorphism group quotients are linear 2-groups.

Describes automorphism group of Rauzy diagrams.

Classifies hyperbolic manifolds with specific automorphism groups.

Study automorphism groups of quandles up to order 10.

In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for $n>3$, $\Aut(P_n)$ is generated by the subgroup $\Aut_c(P_n)$ of central automorphisms of $P_n$, the subgroup $\Aut(B_n)$ of restrictions of automorphisms of $B_n$ on $P_n$ and one extra automorphism $w_n$. W…

For an almost complex structure $J$ in dimension 6 with nondegenerate Nijenhuis tensor $N_J$, the automorphism group $G=Aut(J)$ of maximal dimension is the exceptional Lie group $G_2$. In this paper we establish that the sub-maximal dimension of automorphism groups of almost complex structures with nondegenerate $N_J$,…

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 examines how automorphism growth rates of a group can be deduced from its simpler decompositions.

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

Using the Guirardel-Levitt outer space of a free product, we prove that the outer automorphism group of the outer automorphism group of the universal Coxeter group of rank $n \geq 5$ is trivial, and that it is a cyclic group of order 2 if $n=4$. In addition we prove that the outer automorphism group of the automorphism…

Compact groups can be represented as dessin automorphisms.

Paper describes invariants of slice regular functions' automorphism group.

We discuss the possibility of lifting finite subgroups, and in particular finite cyclic subgroups, with respect to the canonical projections between automorphism and outer automorphism groups of free groups, surface groups and their abelianizations.

Finite groups can be represented as origami automorphisms, extended to countable groups.

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

For an almost product structure $J$ on a manifold $M$ of dimension $6$ with non-degenerate Nijenhuis tensor $N_J$, we show that the automorphism group $G=Aut(M,J)$ has dimension at most 14. In the case of equality $G$ is the exceptional Lie group $G_2^*$. The next possible symmetry dimension is proved to be equal to 10…

Study automorphism groups of Inoue surfaces using quadratic number fields.

Automorphisms of fine curve graph match surface homeomorphisms.

New criterion for bi-ordering free groups under automorphisms.

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…