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Metric and Topological Approaches to Network Data AnalysisChowdhury, Samir 03 September 2019 (has links)
No description available.
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Hodge decompositions and computational electromagneticsKotiuga, Peter Robert. January 1984 (has links)
No description available.
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A study of HomologySchnurr, Michael Anthony 03 June 2013 (has links)
No description available.
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The Construction of Khovanov HomologyLiu, Shiaohan 01 December 2023 (has links) (PDF)
Knot theory is a rich topic in topology that studies the how circles can be embedded in Euclidean 3-space. One of the main questions in knot theory is how to distinguish between different types of knots efficiently. One way to approach this problem is to study knot invariants, which are properties of knots that do not change under a standard set of deformations. We give a brief overview of basic knot theory, and examine a specific knot invariant known as Khovanov homology. Khovanov homology is a homological invariant that refines the Jones polynomial, another knot invariant that assigns a Laurent polynomial to a knot. Dror Bar-Natan wrote a paper in 2002 that explains the construction of Khovanov homology and proves that it is an invariant. We follow his lead and attempt to clarify and explain his formulation in more precise detail.
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On ℓ<sup>2</sup>-homology of low dimensional buildingsBoros, Dan 06 November 2003 (has links)
No description available.
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Profinite groupsGanong, Richard. January 1970 (has links)
No description available.
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Free pro-C groups.Lim, Chong-keang. January 1971 (has links)
No description available.
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Homology of Group Von Neumann AlgebrasMattox, Wade 08 August 2012 (has links)
In this paper the following conjecture is studied: the group von Neumann algebra N(G) is a flat CG-module if and only if the group G is locally virtually cyclic. This paper proves that if G is locally virtually cyclic, then N(G) is flat as a CG-module. The converse is proved for the class of all elementary amenable groups without infinite locally finite subgroups. Foundational cases for which the conjecture is shown to be true are the groups G=Z, G=ZxZ, G=Z*Z, Baumslag-Solitar groups, and some infinitely-presented variations of Baumslag-Solitar groups. Modules other than N(G), such as L^p-spaces and group C*-algebras, are considered as well. The primary tool that is used to achieve many of these results is group homology. / Ph. D.
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Multidimensional Behavioral ComplexesBoquet, Grant Michael 11 April 2008 (has links)
In a preprint by J. Wood, V. Lomadze, and E. Rogers, chains and boundary maps were defined for 2-D discrete behavioral systems. The corresponding homology groups were studied and tied to trajectory properties. Indeed, the homology groups encapsulated the concepts of autonomy, controllability, and signal restriction.
We shall present an extension of their work to n-D discrete behavioral systems. In particular, we shall streamline the construction of the chain groups, the boundary maps between chains, and the study of the resultant homology groups. While constructing this machinery, we shall point out intrinsic flaws in their approach that make extension of their results less systematic. Finishing remarks shall be made on using the homology groups to determine system properties and potentially classify forms of controllability. / Master of Science
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Relating Khovanov homology to a diagramless homologyMcDougall, Adam Corey 01 July 2010 (has links)
A homology theory is defined for equivalence classes of links under isotopy in the 3-sphere. Chain modules for a link L are generated by certain surfaces whose boundary is L, using surface signature as the homological grading. In the end, the diagramless homology of a link is found to be equal to some number of copies of the Khovanov homology of that link. There is also a discussion of how one would generalize the diagramless homology theory (hence the theory of Khovanov homology) to links in arbitrary closed oriented 3-manifolds.
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