In mathematics, a cubical complex (also called cubical set and Cartesian complex) is a set composed of points, line segments, squares, cubes, and their...

showed that a cubical complex (that is, a family of hypercubes intersecting face-to-face) forms a CAT(0) space if and only if the complex is simply connected...

linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes), k-chains are combinations of k-simplices...

a chain complex. Another equivalent statement is that B k {\displaystyle B_{k}} is contained in Z k {\displaystyle Z_{k}} . A cubical complex is a set...

Alexander; Ziegler, Günter M. (2004), "Construction techniques for cubical complexes, odd cubical 4-polytopes, and prescribed dual manifolds", Experimental Mathematics...

R. (2011). Nonabelian Algebraic Topology:filtered spaces, crossed complexes, cubical homotopy groupoids. European Mathematical Society Tracts in Mathematics...

shown that F acts as deck transformations on a locally finite CAT(0) cubical complex (necessarily of infinite dimension). A consequence is that F satisfies...

) {\displaystyle \pi _{1}(M)} . A finite locally connected CAT(0) cubical complex is a classifying space of its fundamental group. The infinite-dimensional...

image at right. Mathematics portal Simplicial complex Cubical complex Reinhard Klette: Cell complexes through time. http://spie.org/Publications/Proceedings/Paper/10...

p} in these balls is convex. Cotangent bundle Covariant derivative Cubical complex Cut locus Diameter of a metric space is the supremum of distances between...

S'{}^{2}\rangle } is of spherical type. Such groups act cocompactly on a CAT(0) cubical complex, and, as a consequence, one can find a rational normal form for their...

six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles. The tesseract is one of the six convex...

{Conf} _{n}(\Gamma )} deformation retract to non-positively curved cubical complexes of dimension at most min ( n , b ( Γ ) ) {\displaystyle \min(n,b(\Gamma...

(gigabyte-scale) grayscale image data in dimension 1, 2 or 3 using cubical complexes and discrete Morse theory. Another R package, TDAstats, uses the Ripser...

discontinuously and cocompactly on a geodetically complete CAT(0) cubical complex X, then either X splits as a direct product of two unbounded convex...

Interdisciplinary Applied Mathematics, Springer, Section 9.4, Weak Orders and Cubical Complexes, pp. 188–196. Ziegler, Günter M. (1995), Lectures on Polytopes, Graduate...

University of Côte d'Azur. Her research involves low-dimensional geometry, cubical complexes, and geometric group theory. She has also studied sexism and institutional...

gained notice for its simple, functional Bauhaus design with its mainly cubical buildings made of reinforced concrete and steel trusses. The shaft's characteristic...

Construx feature beam-like pieces of varying lengths that snapped on to cubical connector knots in order to build large shapes. These are relatively secure...

regular octahedron. The cube can be represented in many ways, such as the cubical graph, which can be constructed by using the Cartesian product of graphs...

applications. The study of group actions on CAT(0) spaces and CAT(0) cubical complexes, motivated by ideas from Alexandrov geometry. Interactions with low-dimensional...

"Improved approximate rips filtrations with shifted integer lattices and cubical complexes". Journal of Applied and Computational Topology. 5 (3): 425–458. doi:10...

are especially abundant in epithelial tissues. They consist of protein complexes and provide contact between neighbouring cells, between a cell and the...

acting properly on simply connected C A T ( 0 ) {\displaystyle CAT(0)} cubical complexes. Groups that admit a finite presentation with only one relation. Discrete...

Rafael (2011). Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids. Tracts in Mathematics. Vol. 15. Zurich: European...

rational coefficients have roots that are irrational (and even non-real) complex numbers. Cubic equations were known to the ancient Babylonians, Greeks...

Vishnu in Hampi. The 3 metres (9.8 ft) Shiva Linga stands in water in a cubical chamber and has three eyes sketched on its top. South of this is the shrine...

large cubical sukanasa containing a Surya (Sun god) icon. Much of the Badigargudi relief artwork has been damaged and eroded. The Durga temple complex houses...

3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry: 3-manifolds, Right-angled Artin Groups, and Cubical Geometry. American Mathematical Soc....

group is a key object in the version of discrete Morse theory for cubical complexes developed by Mladen Bestvina and Noel Brady and in the study of subgroups...