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We prove that simply connected open Riemannian manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.
We show that any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image. This generalizes work of Etingof, Rowell and Witherspoon showing that the braid group images…
We compare some natural triangulations of the Teichm\"uller space of hyperbolic surfaces with geodesic boundary and of some bordifications. We adapt Scannell-Wolf's proof to show that grafting semi-infinite cylinders at the ends of…
We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…
We define mutation pair in a pseudo-triangulated category. We prove that under certain conditions, for a mutation pair in a pseudo-triangulated category, the corresponding quotient category carries a natural triangulated structure. This…
In this short note, we classify the degree-inverting involution on the full square and triangular matrices.
We construct a bijective correspondence between the set of rigid modules over a gentle algebra and the set of admissible arc systems on the associated coordinated-marked surface. In particular, a maximal rigid module aligns with an…
We introduce a notion of mutation for $\tau$-exceptional sequences of modules over arbitrary finite dimensional algebras. For hereditary algebras, we show that this coincides with the classical mutation of exceptional sequences. For rank…
The full resurgent trans-series is found exactly in near-supersymmetric $\mathbb C P^1$ quantum mechanics. By expanding in powers of the SUSY breaking deformation parameter, we obtain the first and second expansion coefficients of the…
A triangulation of a punctured or pinched surface is irreducible if no edge can be shrunk without producing multiple edges or changing the topological type of the surface. The finiteness of the set of (non-isomorphic) irreducible…
We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…
In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and…
We introduce a notion of degenerations of graded modules. In relation to it, we also introduce several partial orders as graded analogies of the hom order, the degeneration order and the extension order. We prove that these orders are…
We introduce the notion of composition series of triangulated categories, which generalizes full exceptional sequences. The lengths of composition series yield invariants for triangulated categories. We study composition series of derived…
We describe some theoretical results on triangulations of surfaces and we develop a theory on roots, decompositions and genus-surfaces. We apply this theory to describe an algorithm to list all triangulations of closed surfaces with at most…
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets.…
In this article we study certain notions of `tameness' for the persistence modules studied in topological data analysis. In particular, we show that after adding infinitary points the so called finitely determined modules become finitely…
We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a question of Cameron. We also arrive at a natural description of all…