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Now showing items 1-9 of 9

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    A recursive formula for the Khovanov cohomology of a family of 3-stranded pretzel knots 

    Meier, Jeffrey (2009)
    After reviewing the process of associating graded cohomology groups (Khovanov cohomology) to a knot, we prove two lemmas that reduce the computational complexity of calculating the Khovanov cohomology. We then prove a ...
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    Combinatorial Knot Floer Homology 

    Nair, Divya Sukumaran (2012)
    Knot Floer Homology HFK(K) of a knot K in S^3 was defined by Peter Ozsváth and Zoltan Szabó in 2003. It has since become powerful invariant for the study of properties of knots. The definition of the Knot Floer Homology ...
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    Galileo's Assayer: Sense and Reason in the Epistemic Balance 

    Smith, James Adam (2018)
    Galileo’s The Assayer, published in 1623, represents a turning point in Galileo’s philosophicalwork. A highly polemic “scientific manifesto,” The Assayer was written afterhis astronomical discoveries of the moons of Jupiter ...
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    Geometric, Algebraic, and Topological Connections in the Historical Sphere of the Platonic Solids 

    Smith, James Adam (2012)
    The Platonic solids have made prominent appearances in the history of pure mathematics: in Euclid's <italic>Elements</italic>, which contains early geometric constructions of the solids and demonstrates the special manner ...
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    Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots 

    Gafney, T.J. (2011)
    Symmetric unions, originally introduced in 1957 by Shin’ichi Kinoshita and Hide- taka Terasaka [3], have since been studied due to their failure to be distinguished by some invariants. In his 2000 paper, Mikhail Khovanov ...
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    Knot Groups and Their Homomorphisms into SU(2) 

    DeBolt, Rashelle (2019)
    We begin with an introduction to algebraic topology, knot theory, and SU(2) matrices as a subset of the quaternions, then proceed to introduce a technique of finding homomorphisms of knot complement fundamental groups into ...
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    Rational Witt Classes of 4-Stranded Pretzel Knots 

    Kelly, Tynan Blaine (2010)
    The rational Witt classes of knots are invariants related to knot concordance. Although they are somewhat weaker than other concordance invariants, for example, the algebraic concordance classes, they are much easier to ...
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    The Homotopy Theory of Commutative dg Algebras and Representability Theorems for Lie Algebra Cohomology 

    Ozbek, Aydin (2019)
    Building on the seminal works of Quillen and Sullivan, Bousfield and Guggenheim developed a "homotopy theory" for commutative differential graded algebras (cdgas) in order to study the rational homotopy theory of topological ...
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    Topology Counterparts in C*-Algebras 

    Corder, Daniel Surrell (2013)
    This paper describes a contravariant category equivalence between the category of unital commutative C*-algebras with unital *-homomorphisms and the category of compact Hausdorff spaces with continuous functions in order ...