Related papers: A family of pseudo-Anosov braids whose super summi…
We give sufficient conditions for an expansive partially hyperbolic diffeomorphism with one-dimensional center to be (topologically) Anosov.
Given a finite generating set $S$, let us endow the mapping class group of a closed hyperbolic surface with the word metric for $S$. We discuss the following question: does the proportion of non-pseudo-Anosov mapping classes in the ball of…
We investigate a lattice model of comb polymers and derive bounds on the exponential growth rate of the number of embeddings of the comb. A comb is composed of a backbone that is a self-avoiding walk and a set of $t$ teeth, also modelled as…
We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the…
Recently, Okounkov, Lazarsfeld and Mustata, and Kaveh and Khovanskii have shown that the growth of a graded linear series on a projective variety over an algebraically closed field is asymptotic to a polynomial. We give a complete…
In the hyperspace of subcontinua of a compact surface we consider a second order Hausdorff distance. This metric space is compactified in such a way that the stable foliation of a pseudo-Anosov map is naturally identified with a…
Certain families of manifolds which support Anosov flows do not support expanding, quasi-isometric foliations.
It is well-known that there is a faithful representation of braid groups on automorphism groups of free groups, and it is also well-known that free groups are bi-orderable. We investigate which n-strand braids give rise to automorphisms…
We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for nontrivial finite quotients of the commutator subgroup of the…
In this paper we study the growth rates of Artin monoids and we show that 4 is a universal upper bound. We also show that the generating functions of the associated right-angled Artin monoids are given by families of Chebyshev polynomials.…
We estimate the size of a labelled tree by comparing the amount of (labelled) nodes with the size of the set of labels. Roughly speaking, a exponentially big labelled tree, is any labelled tree that has an exponential gap between its size,…
A.Regev proved that the codimension growth of an associative PI-algebra is at most exponential. The author established a scale for the codimension growth of Lie PI-algebras, which includes a series of functions between exponential and…
Let X be a hyperbolic surface and H the fundamental group of a hyperbolic 3-manifold that fibers over the circle with fiber X. Using the Birman exact sequence, H embeds in the mapping class group Mod(Y) of the surface Y obtained by removing…
We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…
Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost transverse to a quasigeodesic pseudo-Anosov flow. We show that the leaves of the foliation in the universal cover extend…
We introduce a family of automorphisms on the bosonic extension of arbitrary type and show that they satisfy the braid relations. They preserve the global basis and the crystal basis. Using this braid group action, we define a subalgebra…
We prove polynomial upper bounds on the growth of solutions to 2d cubic NLS where the Laplacian is confined by the harmonic potential. Due to better bilinear effects our bounds improve on those available for the $2d$ cubic NLS in the…
We show that every group in a large family of (not necessarily torsion) spinal groups acting on the ternary rooted tree is of subexponential growth.
Given any generating set of any pseudo-Anosov-containing subgroup of the mapping class group of a surface, we construct a pseudo-Anosov with word length bounded by a constant depending only on the surface. More generally, in any subgroup G…
An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere S is constructed, and their invariant foliations and singular orbits are described explicitly by means of generalized train tracks. The complex strucure induced by…