Related papers: Cataloguing PL 4-manifolds by gem-complexity
This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be…
Haefliger-Thurston's conjecture predicts that Haefliger's classifying space for $C^r$-foliations of codimension $n$ whose normal bundles are trivial is $2n$-connected. In this paper, we confirm this conjecture for PL foliations of…
We solve the isomorphism problem for the whole class of Lins-Mandel gems (graphs encoded manifolds). We also present certain homeomorphisms of branched cyclic coverings of two-bridge hyperbolic links. As a consequence, we prove that, in in…
Markov proved that there exists an unrecognizable 4-manifold, that is, a 4-manifold for which the homeomorphism problem is undecidable. In this paper we consider the question how close we can get to S^4 with an unrecognizable manifold. One…
We classify all wormhole singularities, i.e. cyclic quotient surface singularities admitting at least two extremal P-resolutions, thereby solving an open problem posed by Urz\'ua. Our approach introduces a new combinatorial framework based…
Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle finding) as well as triangle enumeration (triangle listing) play central roles in the field of graph algorithms. In distributed computing,…
A graph G is prismatic if for every triangle T of G, every vertex of G not in T has a unique neighbour in T. The complement of a prismatic graph is called \emph{antiprismatic}. The complexity of colouring antiprismatic graphs is still…
Clique-width is one of the graph complexity measures leading to polynomial special-case algorithms for generally NP-complete problems, e.g. graph colourability. The best two currently known algorithms for verifying c-colourability of graphs…
We develop a localisation theory for certain categories, yielding a 3-arrow calculus: Every morphism in the localisation is represented by a diagram of length 3, and two such diagrams represent the same morphism if and only if they can be…
The chromatic number for properly colouring the facets of a combinatorial simple $n$-polytope $P^n$ that is the orbit space of a quasitoric manifold satisfies the inequality $n\leq P^n\leq 2^n-1$. The inequality is sharp for $n=2$ but not…
Let $G$ be a simply connected solvable Lie group with a lattice $\Gamma$ and $N$ the nilradical of $G$. For a complex valued representation $\rho: G\to GL(V_{\rho})$ such that the restriction $\rho_{|_{N}}$ is unipotent, as an advanced…
The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in two earlier papers (math.SG/0101206 and math.SG/0105202). This four-dimensional theory also…
Automatic marbles classification based on their visual appearance is an important industrial issue. However, there is no definitive solution to the problem mainly due to the presence of randomly distributed high number of different colours…
Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…
Scheme-theoretic methods are used to classify ternary quadratic forms with values in line bundles over arbitrary schemes and to canonically determine the isomorphisms between them. The association of a quadratic bundle to its even Clifford…
We consider mapping class groups \Gamma(M) = pi_0 Diff(M fix \partial M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres. We show that if M contains CP^2 (with either orientation) as a…
A crystallization of a PL manifold is an edge-colored graph encoding a contracted triangulation of the manifold. The concept of regular genus generalizes the notions of surface genus and Heegaard genus for 3-manifolds to higher-dimensional…
We classify topological $4$-manifolds with boundary and fundamental group $\mathbb{Z}$, under some assumptions on the boundary. We apply this to classify surfaces in simply-connected $4$-manifolds with $S^3$ boundary, where the fundamental…
Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed…
We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…