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In this paper, we investigate the homotopy type and combinatorial properties of total cut complexes of squared cycle graphs. The total cut complexes are a new type of graphical complexes introduced by Bayer et al.(2024) to extend…
Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point…
We classify homotopes of classical symmetric spaces (studied in Part I of this work). Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers, over a non-degenerate base; the base…
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW complex. As a corollary we obtain that the integer cohomology of these spaces is torsion free. We use Discrete Morse Theory, providing a sequence of…
Interpreting the small-scale clustering of galaxies with halo models can elucidate the connection between galaxies and dark matter halos. Unfortunately, the modelling is typically not sufficiently accurate for ruling out models…
We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular this allows us to characterize the homotopy colimits of diagrams of…
We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our…
We consider random conformally invariant paths in the complex plane (SLEs). Using the Coulomb gas method in conformal field theory, we rederive the mixed multifractal exponents associated with both the harmonic measure and winding (rotation…
Incidence relations among the cells of a regular CW complex produce a poset-enriched category of entrance paths whose classifying space is homotopy-equivalent to that complex. We show here that each acyclic partial matching (in the sense of…
Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at…
The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a…
We report on a study of young star cluster complexes in the spiral galaxy M51. Recent studies have confirmed that star clusters do not form in isolation, but instead tend to form in larger groupings or complexes. We use {\it HST} broad and…
Given a CW-complex A we define an `A-shaped' homology theory which behaves nicely towards A-homotopy groups allowing the generalization of many classical results. We also develop a relative version of the Federer spectral sequence for…
In this paper, I review to what extent we can understand the photometric properties of star clusters, and of low-mass, unresolved galaxies, in terms of population synthesis models designed to describe `simple stellar populations' (SSPs),…
Given two discrete Morse functions on a simplicial complex, we introduce the {\em connectedness homomorphism} between the corresponding discrete Morse complexes. This concept leads to a novel framework for studying the connectedness in…
Given an algebraic theory $\ct$, a homotopy $\ct$-algebra is a simplicial set where all equations from $\ct$ hold up to homotopy. All homotopy $\ct$-algebras form a homotopy variety. We give a characterization of homotopy varieties…
Using the 2MASS Photometric Redshift catalogue we perform a number of statistical tests aimed at detecting possible departures from statistical homogeneity and isotropy in the large-scale structure of the Universe. Making use of the angular…
In this paper we study the global structure of the stable homotopy theory of spectra. We establish criteria for when the homotopy theory associated to a given stable model category agrees with the classical stable homotopy theory of…
We construct models describing the velocity field in the infall regions of clusters. The velocity field is the superposition of a systematic component and a "noise" component accounting for the effects of small scale substructure and…
The perfect matching complex of a simple graph $G$ is a simplicial complex having facets (maximal faces) as the perfect matchings of $G$. This article discusses the perfect matching complex of polygonal line tilings and the $\left(2 \times…