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dc.contributor.advisorOzsvath, Peter S
dc.contributor.authorHugelmeyer, Cole Wilkening
dc.contributor.otherMathematics Department
dc.description.abstractWe present various generalizations of the finite type theory of knots by establishing a relationship between generalized finite type theories of knot-like structures and diagrammatic combinatorial systems for representing those structures. By inventing suitable new combinatorial diagram systems for representing knots and knot-like structures, we can compute generalized finite type theories. We will create a category theoretical formalization of this correspondence, and demonstrate it through three examples: the standard finite type theory and its relationship with clasp diagrams, the finite type theory of delta moves and a new diagram system called looms, and the finite type theory of combinatorial structures we call virtual transverse knots. The finite type theory of delta moves may have applications to unknotting number, and the theory of virtual transverse knots leads to many interesting and difficult conjectures. Finally, we will go beyond finite type theories to study how our formalization can be applied more generally.
dc.publisherPrinceton, NJ : Princeton University
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: <a href=></a>
dc.subjectdelta moves
dc.subjectfinite type invariants
dc.subjectknot theory
dc.subjectstate sum invariants
dc.subjecttransverse knots
dc.subjectvirtual knots
dc.titleGeneralized State-Sum Invariants of Knots
dc.typeAcademic dissertations (Ph.D.)
Appears in Collections:Mathematics

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