相关论文: On the annulus complex of a handlebody

Le but cette note est de tenter d'expliquer les liens \'etroits qui unissent la th\'eorie des empilements de cercles et des modules combinatoires, et de comparer les approches \`a la conjecture de J.W. Cannon qui en d\'ecoulent. ???? The…

In this article, we prove a combination theorem for a complex of relatively hyperbolic groups. It is a generalization of Martin's \cite{martin} work for combination of hyperbolic groups over a finite $M_K$-simplicial complex, where $k\leq…

In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.

We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise…

Let M be a connected orientable 3-manifold, and F a compact connected orientable surface properly embedded in M. If F cuts M into two connected 3-manifolds X and Y, that is, M=X \cup_F Y, we say that M is an amalgamation of X and Y along F;…

This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial…

This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…

Given a finite ribbon category, which is a particular case of a cyclic algebra over the operad of genus zero surfaces, there are two possibilities for an extension defined on all three-dimensional handlebodies: On the one hand, one can use…

We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or…

We explain how to construct certain potential functions for the hyperbolic structures of a knot complement, which are closely related to the analytic functions on the deformation space of hyperbolic structures.

This re-certifying paper describes the details of the Morse homology of manifolds with boundary, introduced by the author before, in terms of handlebody decompositions.

We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…

We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable…

We develop a tighter implementation of basic PL topology, which keeps track of some combinatorial structure beyond PL homeomorphism type. With this technique we clarify some aspects of PL transversality and give combinatorial proofs of a…

We develop a word mechanism applied in knot and link diagrams for the illustration of a diagrammatic property. We also give a necessary condition for determining incompressible and pairwise incompressible surfaces, that are embedded in knot…

In this study, the properties of an oscillating system composed of a pendulum connected to a seesaw and placed on a moving platform with a certain slope are analyzed. Using complex numbers to collect the information contained in the system…

We show that any simple holomorphic disc admits the annulus property, i.e., each interior point is surrounded by an arbitrary small annulus consisting entirely of injective points. As an application we show that interior singularities of…

We prove a formula for the conjugation action on the knot Floer complex of the connected sum of two knots. Using the formula we construct a homomorphism from the smooth concordance group to an abelian group consisting of chain complexes…

We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces,…

In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic…