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Showing 1 to 20 of 68 for “"Homological"”.
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Homological algebra
… directly relate with the functor Ext used in homological algebra."--Document.</p>
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Homological properties of determinantal arrangements
<p>We study a certain family of hypersurface arrangements known as determinantal arrangements. Determinantal arrangements are a union of varieties defined by minors of a matrix of indeterminates. In particular, we investigate determinantal arrangements using the 2-minors of a 2 × <em>n</em> generic …
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Homological Illusions of Persistence and Stability
<p>In this thesis we explore and extend the theory of persistent homology, which captures topological features of a function by pairing its critical values. The result is represented by a collection of points in the extended plane called persistence diagram.</p><p>We start with the question of …
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Homological invariants of some special varieties
… we discuss several different results about some homological invariants (e.g., graded Betti numbers, Hilbert function, regularity) of some special varieties. In particular, we focus on the codimension two ACM varieties in P1×P1×P1 (called varieties of lines), and the edge ideals of bicyclic …
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Some Duality Results in Homological Algebra
Finally, we examine local cohomology involving square-free monomial ideals. We provide an alternate proof of one of Mustataˇ's constructions for computing H˙IR and use it to provide a simpler proof of E. Miller's duality result relating H˙IR to H˙m R/I , also showing that the …
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Certifying homological algorithms to study biomedical images
En esta tesis se aborda el problema de la verificación de programas para el procesamiento homológico de imágenes biomédicas. Concretamente, se formalizan en la herramienta de demostración Coq/SSReflect algoritmos para el cálculo de grupos de homología, lo que produce programas ejecutables que son …
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On Bredon (co-)homological dimensions of groups
… way to attack this question is using methods in homological algebra. The natural choice for a cohomology theory to study G-CW-complexes with stabilisers in a given family F is known as Bredon cohomology. It is the study of cohomology in the category of OFG-modules. This category relates to models …
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Applications of Homological Algebra to Equational Theories
… theory (or term rewriting system), using homological algebra. Their method is an analog of Squier’s homology theory on string rewriting systems. In this dissertation, I develop the homology theory for term rewriting systems more and provide a better lower bound under a stronger notion of …
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Homological classification of monoids by projectivities of right acts
Die Darstellung von Monoiden durch Transformationen von Mengen, die zu Akten über Monoiden führt, ist die Basis dieser Dissertation. Eine große Anzahl von Ergebnissen über Akte über Monoiden beziehen sich auf Fragen der homologischen Klassifikation, in der Eigenschaften von Akten über einem Monoid …
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Homological stability of spaces of manifolds via E_k-algebras
In this thesis we study homological stability properties of different families of spaces using the technique of cellular *E<sub>k</sub>*-algebras. Firstly, we will consider spin mapping class groups of surfaces, and their algebraic analogue —quadratic symplectic groups— using cellular …
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A study of homological invariants modulo an exact zero divisor
… of this construction to the study of several homological invariants, such as complexity, curvature and generalized Poincaré series.
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Parallelization strategies for extraction of (co)homological information of digital objects.
Un objeto digital es un conjunto de n-xels en de una imagen digital n-dimensional. El estudio de la conectividad de estos objetos, interpretados de manera discreta, subdividida o continua, ha sido una custión prioritaria desde los inicios del tratamiento de Imagen Digital. Las herramientas …
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Geometric and homological methods in group theory: constructing small group resolutions
Given two groups K and H for which we have the free crossed resolutions, B* --> K and C* --> H respectively. Our aim is to construct a free crossed resolution, A* --> G, by way of induction on the degree n, for any semidirect product G = K x H. First we show how to find a set Z1 of generators for …
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Homological mirror symmetry for a Calabi-Yau hypersurface in projective space
This thesis is concerned with Kontsevich's Homological Mirror Symmetry conjecture. In Chapter 1, which is based on [1], we consider the n-dimensional pair of pants, which is defined to be the complement of n + 2 generic hyperplanes in CPn. The pair of pants is conjectured to be mirror to the …
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From Homological Algebra To Topology via Type B Zigzag Algebra and Heisenberg Algebra
We construct a faithful categorical action of the type $B$ braid group on the bounded homotopy category of finitely generated projective modules over a finite dimensional algebra which we call the type $B$ zigzag algebra. This categorical action is closely related to the action of the type $B$ …
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From Homological Algebra To Topology via Type B Zigzag Algebra and Heisenberg Algebra
We construct a faithful categorical action of the type $B$ braid group on the bounded homotopy category of finitely generated projective modules over a finite dimensional algebra which we call the type $B$ zigzag algebra. This categorical action is closely related to the action of the type $B$ …
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Razonamiento mecanizado en álgebra homológica
… version of a crucial algorithm in the field of Homological Algebra, known as "Perturbation Lemma". This lemma is intensively used in the software system "Kenzo", devoted to symbolic computation in Homological Algebra. To this end, we use the proof assistant "Isabelle". Our main motivations are …
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On Gorenstein Projective and Gorenstein Flat Modules
… metatheorem states, "Every result in classical homological algebra has a counterpart in Gorenstein homological algebra". We support this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This …
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Higher Scissors Congruence Groups of the Euclidean Plane
… congruence groups are uncountable. Applying homological methods here will shed light on a conjecture that says a homological tool called a trace map detects all higher scissors congruence groups. To prove or disprove this conjecture would be a great achievement for understanding the interface …
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