Related papers: A characterization of alternating link exteriors i…
Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of…
We define a new kind of algebroid which fulfills a Leibniz rule, a Jacobi identity twisted by a 3-form $H$ with values in the kernel of the anchor map, and the twist is closed under a naturally occurring exterior covariant derivative. We…
This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…
A special subcomplex of the singular chain complex for a topological space, historically called oriented singular chain complex is used here with the new name "alternative" singular chain complex. It was already known that this subcomplex…
We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum $\mathfrak{sl}_N$, their duals, and their direct sums. We show that the first two…
This article introduces descriptive cellular homology on cell complexes, which is an extension of J.H.C. Whitehead's CW topology. A main result is that a descriptive cellular complex is a topology on fibres in a fibre bundle. An application…
In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of…
The interior polynomial is an invariant of bipartite graphs, and a part of the HOMFLY polynomial of a special alternating link coincides with the interior polynomial of the Seifert graph of the link. We extend the interior polynomial to…
In this paper, we introduce the concept and representation of modified $\lambda$-differential Lie triple systems. Next, we define the cohomology of modified $\lambda$-differential Lie triple systems with coefficients in a suitable…
In the present note we study combinatorial and algebraic properties of cubic-line arrangements in the complex projective plane admitting nodes, ordinary triple and $A_{5}$ singular points. We deliver a Hirzebruch-type inequality for such…
We classify exterior fibrations in the exterior homotopy category. As a result we also classify proper fibrations between CW-complexes.
We introduce the class of outerspatial 2-complexes as the natural generalisation of the class of outerplanar graphs to three dimensions. Answering a question of O-joung Kwon, we prove that a locally 2-connected 2-complex is outerspatial if…
We study the homeomorphism types of certain covers of (always orientable) surfaces, usually of infinite-type. We show that every surface with non-abelian fundamental group is covered by every noncompact surface, we identify the universal…
In this note, we give a motivic characterization of the integral cohomology of dual boundary complexes of smooth quasi-projective complex algebraic varieties. As a corollary, the dual boundary complex of any stably affine space (of positive…
A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…
Given a prime, alternating link diagram, we build a special cover of the link complement whose degree is bounded by a factorial function of the crossing number. It follows that a subgroup of the link group of that index embeds into…
The geometry of an admissible B\"acklund transformation for an exterior differential system is described by an admissible Cartan connection for a geometric structure on a tower with infinite--dimensional skeleton which is the universal…
We show that one can interweave an unknot into any non-alternating connected projection of a link so that the resulting augmented projection is alternating.
A concept of implicit links for Complex Networks has been defined and a new value - cohesion factor, which allows to evaluate numerically the presence of such connection between any two nodes, has been introduced. We introduce a…
We provide a canonical form of mixed states in bipartite quantum systems in terms of a convex combination of a separable state and a, so-called, edge state. We construct entanglement witnesses for all edge states. We present a canonical…