Relevant bibliographies by topics / Cochain complexes

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Cochain complexes'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 January 2023

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Journal articles on the topic "Cochain complexes"

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Larsen, Michael, and Ayelet Lindenstrauss. "Coxeter cochain complexes." Israel Journal of Mathematics 203, no. 1 (2014): 173–87. http://dx.doi.org/10.1007/s11856-014-0034-2.

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Falk, Richard S., and Ragnar Winther. "Double complexes and local cochain projections." Numerical Methods for Partial Differential Equations 31, no. 2 (2014): 541–51. http://dx.doi.org/10.1002/num.21922.

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Lee, Dae-Woong. "On the Digital Cohomology Modules." Mathematics 8, no. 9 (2020): 1451. http://dx.doi.org/10.3390/math8091451.

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In this paper, we consider the digital cohomology modules of a digital image consisting of a bounded and finite subset of Zn and an adjacency relation. We construct a contravariant functor from the category of digital images and digital continuous functions to the category of unitary R-modules and R-module homomorphisms via the category of cochain complexes of R-modules and cochain maps, where R is a commutative ring with identity 1R. We also examine the digital primitive cohomology classes based on digital images and find the relationship between R-module homomorphisms of digital cohomology m
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Sharko, V. V. "Numerical invariants of cochain complexes and the Morse numbers of manifolds." Proceedings of the Steklov Institute of Mathematics 252, no. 1 (2006): 248–63. http://dx.doi.org/10.1134/s0081543806010214.

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Richter, Birgit, and Steffen Sagave. "A strictly commutative model for the cochain algebra of a space." Compositio Mathematica 156, no. 8 (2020): 1718–43. http://dx.doi.org/10.1112/s0010437x20007319.

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AbstractThe commutative differential graded algebra $A_{\mathrm {PL}}(X)$ of polynomial forms on a simplicial set $X$ is a crucial tool in rational homotopy theory. In this note, we construct an integral version $A^{\mathcal {I}}(X)$ of $A_{\mathrm {PL}}(X)$. Our approach uses diagrams of chain complexes indexed by the category of finite sets and injections $\mathcal {I}$ to model $E_{\infty }$ differential graded algebras (dga) by strictly commutative objects, called commutative $\mathcal {I}$-dgas. We define a functor $A^{\mathcal {I}}$ from simplicial sets to commutative $\mathcal {I}$-dgas
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Hüttemann, Thomas, and David Quinn. "Finite domination and Novikov rings: Laurent polynomial rings in two variables." Journal of Algebra and Its Applications 14, no. 04 (2015): 1550055. http://dx.doi.org/10.1142/s0219498815500553.

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Let C be a bounded cochain complex of finitely generated free modules over the Laurent polynomial ring L = R[x, x-1, y, y-1]. The complex C is called R-finitely dominated if it is homotopy equivalent over R to a bounded complex of finitely generated projective R-modules. Our main result characterizes R-finitely dominated complexes in terms of Novikov cohomology: C is R-finitely dominated if and only if eight complexes derived from C are acyclic; these complexes are C ⊗L R〚x, y〛[(xy)-1] and C ⊗L R[x, x-1]〚y〛[y-1], and their variants obtained by swapping x and y, and replacing either indetermina
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CHRISTIANSEN, SNORRE H. "A CONSTRUCTION OF SPACES OF COMPATIBLE DIFFERENTIAL FORMS ON CELLULAR COMPLEXES." Mathematical Models and Methods in Applied Sciences 18, no. 05 (2008): 739–57. http://dx.doi.org/10.1142/s021820250800284x.

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Given a cellular complex, we construct spaces of differential forms which form a complex under the exterior derivative, which is isomorphic to the cochain complex of the cellular complex. The construction applies in particular to subsets of Euclidean space divided into polyhedra, for which it provides, for each k, a space of k-forms with a basis indexed by the set of k-dimensional cells. In the framework of mimetic finite differences, the construction provides a conforming reconstruction operator. The construction requires auxiliary spaces of differential forms on each cell, for which we provi
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Vrana, Péter, and Máté Farkas. "Homological codes and abelian anyons." Reviews in Mathematical Physics 31, no. 10 (2019): 1950038. http://dx.doi.org/10.1142/s0129055x19500387.

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We study a generalization of Kitaev’s abelian toric code model defined on CW complexes. In this model, qudits are attached to [Formula: see text]-dimensional cells and the interaction is given by generalized star and plaquette operators. These are defined in terms of coboundary and boundary maps in the locally finite cellular cochain complex and the cellular chain complex. We find that the set of energy-minimizing ground states and the types of charges carried by certain localized excitations depends only on the proper homotopy type of the CW complex. As an application, we show that the homolo
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HU, PO. "HIGHER STRING TOPOLOGY ON GENERAL SPACES." Proceedings of the London Mathematical Society 93, no. 2 (2006): 515–44. http://dx.doi.org/10.1112/s0024611506015838.

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In this paper, I give a generalized analogue of the string topology results of Chas and Sullivan, and of Cohen and Jones. For a finite simplicial complex $X$ and $k \geq 1$, I construct a spectrum $Maps(S^k, X)^{S(X)}$, which is obtained by taking a generalization of the Spivak bundle on $X$ (which however is not a stable sphere bundle unless $X$ is a Poincaré space), pulling back to $Maps(S^k, X)$ and quotienting out the section at infinity. I show that the corresponding chain complex is naturally homotopy equivalent to an algebra over the $(k + 1)$-dimensional unframed little disk operad $\m
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Baushi, Arben. "THE MAYER VIETORIS SEQUENCE CALCULATING DE RHAM COHOMOLOGY." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 8 (2016): 6516–21. http://dx.doi.org/10.24297/jam.v12i8.5072.

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De Rham cohomology it is very obvious that it relies heavily on both topology as well as analysis. We can say it creates a natural bridge between the two. To understand and be able to explain what exactly de Rham cohomology is to the world of mathematics we need to know de Rham groups. This is the reasons to calculate the de Rham cohomology of a manifold. This is usually quite difficult to do directly. We work with manifold. Manifold is a generalization of curves and surfaces to arbitrary dimension. A topological space M is called a manifold of dimension k if : · M is a topological Hausdorff
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Dissertations / Theses on the topic "Cochain complexes"

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McBride, Aaron. "Grothendieck Group Decategorifications and Derived Abelian Categories." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/33000.

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The Grothendieck group is an interesting invariant of an exact category. It induces a decategorication from the category of essentially small exact categories (whose morphisms are exact functors) to the category of abelian groups. Similarly, the triangulated Grothendieck group induces a decategorication from the category of essentially small triangulated categories (whose morphisms are triangulated functors) to the category of abelian groups. In the case of an essentially small abelian category, its Grothendieck group and the triangulated Grothendieck group of its bounded derived category are
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Books on the topic "Cochain complexes"

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Ranicki, Andrew. Algebraic L-theory and topological manifolds. Cambridge University Press, 2008.

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Ranicki, Andrew. Algebraic L̲-theory and topological manifolds. Cambridge University Press, 1992.

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Book chapters on the topic "Cochain complexes"

1

"Ordering of functional cochains on a complex domain." In Translations of Mathematical Monographs. American Mathematical Society, 1991. http://dx.doi.org/10.1090/mmono/094/06.

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"Tests on Complete Randomised Blocks: Extensions to the Friedman and Cochran Tests." In A Contingency Table Approach to Nonparametric Testing. Chapman and Hall/CRC, 2000. http://dx.doi.org/10.1201/9781420035957-8.

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3

Lynch, Cecelia. "Friedrich Kratochwil: Prophet of Doubt?" In Praxis as a Perspective on International Politics, edited by Gunther Hellmann, Jens Steffek, Gunther Hellmann, and Jens Steffek. Policy Press, 2022. http://dx.doi.org/10.1332/policypress/9781529220469.003.0003.

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In this chapter, Cecelia Lynch assesses Kratochwil’s conceptions of ‘prophecy’ and religion to highlight insights and tensions vis-à-vis time, history, community of meaning, and certainty for praxis. What fascinates her in particular is the question of how one might think about ‘immanence’ in the theological/philosophical matrix within which Kratochwil theorizes. In putting Kratochwil in conversation on issues of praxis and prophecy with interlocutors like Ian Shapiro and Michael Walzer, but also with selected theologians and social theorists such as Walter Brueggemann and Cornel West, or scholars in the tradition of pragmatism such as Jason Springs and Molly Cochran, Lynch hopes to probe forms of accompaniment with, rather than a complete U-turn from, Kratochwil’s Humean analysis. These contrasts also put into sharper relief demands for action that might differ from Kratochwil’s, especially with regard to multiple precarities that Lynch sees in the contemporary time.
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Conference papers on the topic "Cochain complexes"

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Bonizzoni, F., and G. Kanschat. "H 1 -conforming finite element cochain complexes n cartesian meshes." In 8th European Congress on Computational Methods in Applied Sciences and Engineering. CIMNE, 2022. http://dx.doi.org/10.23967/eccomas.2022.134.

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Wang, Randi, and Vadim Shapiro. "Topological Semantics for Lumped Parameter Systems Modeling." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98181.

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Abstract Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of ordinary differential and algebraic equations. Languages and simulation tools for modeling such systems differ in syntax, informal semantics, and in the methods by which such systems of equations are generated and simulated, leading to numerous interoperability challenges. We propose to unify semantics of all such systems using standard notions from alge
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