Related papers: Small cancellation groups with and without sigma-c…
We study limits of quasifuchsian groups for which the bending measures on the convex hull boundary tend to zero, giving necessary and sufficient conditions for the limit group to exist and be Fuchsian. As an application we complete the…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
In this brief note, we provide an example of non complete locally convex space $E$ with a $\sigma(E, E^*)$ closed bounded subset $C\subset E$, which is not $\sigma(E, E^*)$-compact, even if every $\varphi\in E^*$ attains its sup over $C$.
We present four generalized small cancellation conditions for finite presentations and solve the word- and conjugacy problem in each case. Our conditions $W$ and $W^*$ contain the non-metric small cancellation cases C(6), C(4)T(4), C(3)T(6)…
We study automaton groups without singular points, that is, points in the boundary for which the map that associates to each point its stabilizer, is not continuous. This is motivated by the problem of finding examples of infinite…
The article is devoted to a proof of the optimal upper-bound for Morse Lemma, its "anti"-version and their applications. Roughly speaking, Morse Lemma states that in a hyperbolic metric space, a $\lambda$-quasi-geodesic $\gamma$ sits in a…
We study the manifold of clusters of nonintersecting congruent solid bodies, all touching the central ball $B\subset\mathbb{R}^{3}$ of radius one. Two main examples are clusters of balls and clusters of infinite cylinders. We introduce the…
We consider the Sen limit of several global F-theory compactifications, some of which exhibit an MSSM-like spectrum. We show that these indeed have a consistent limit where they can be viewed as resulting from an intersecting D-brane…
We describe the topological behavior of the conjugacy action of the mapping class group of an orientable infinite-type surface $\Sigma$ on itself. Our main results are: (1) All conjugacy classes of $MCG(\Sigma)$ are meager for every…
In this article, we are interested in metric spaces that satisfy a weak non-positive curvature condition in the sense that they admit a conical geodesic bicombing. We show that the analog of a question of Gromov about compactness properties…
We give, in dimensions three or greater, an example of a bounded, pseudoconvex, circular domain in complex space with smooth real analytic boundary and non-compact automorphism group which is not biholomorphically equivalent to any…
This note gives an overview on the construction of symplectic groupoids as reduced phase spaces of Poisson sigma models and its generalization in the infinite dimensional setting (before reduction).
The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not $4$-dimensional and the $4$-dimensional unit sphere. This class is for higher dimensional…
We give a new construction of a C*-algebra from a cancellative semigroup $P$ via partial isometric representations, generalising the construction from the second named author's thesis. We then study our construction in detail for the…
We consider a finite-dimensional, locally finite CAT(0) cube complex X admitting a co-compact properly discontinuous countable group of automorphisms G. We construct a natural compact metric space B(X) on which G acts by homeomorphisms, the…
We classify minimal transitive subsemigroups of the finitary inverse symmetric semigroup modulo the classification of minimal transitive subgroups of finite symmetric groups; and semitransitive subsemigroups of the finite inverse symmetric…
It is well known that there exist non-isomorphic compact groups with isomorphic representation rings (fusion rules). Nevertheless, considerable structural information about the group can be reconstructed from its representation ring. We…
Let $\Gamma$ be a discrete group. When $\Gamma$ is nonamenable, the reduced and full group $C$*-algebras differ and it is generally believed that there should be many intermediate $C$*-algebras, however few examples are known. In this paper…
Motivated by the problem of characterizing KMS states on the reduced C$^*$-algebras of \'etale groupoids, we show that the reduced norm on these algebras induces a C$^*$-norm on the group algebras of the isotropy groups. This C$^*$-norm…
We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.