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Full-Text Articles in Physical Sciences and Mathematics
Frobenius Objects In The Category Of Relations, Rajan Amit Mehta, Ruoqi Zhang
Frobenius Objects In The Category Of Relations, Rajan Amit Mehta, Ruoqi Zhang
Mathematics Sciences: Faculty Publications
We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special dagger Frobenius objects in the category of relations are in correspondence with groupoids. As an additional example, we construct a Frobenius object in the category of relations whose elements are certain cohomology classes in a compact oriented Riemannian manifold.
Higher Chow Cycles On The Jacobian Of Curves., Subham Sarkar Dr.
Higher Chow Cycles On The Jacobian Of Curves., Subham Sarkar Dr.
Doctoral Theses
The following formula, usually called Beilinson’s formula — though independently due to Deligne as well — describes the motivic cohomology group of a smooth projective variety X over a number field as the group of extensions in a conjectured abelian category of mixed motives, MMQ.The aim of this thesis is to describe this construction in the case of the motivic cohomology group of the Jacobian of a curve. The first work in this direction is due to Harris [Har83] and Pulte [Pul88], [Hai87]. They showed that the Abel-Jacobi image of the modified diagonal cycle on the triple product of a …
Non-Associative Algebraic Structures In Knot Theory, Emanuele Zappala
Non-Associative Algebraic Structures In Knot Theory, Emanuele Zappala
USF Tampa Graduate Theses and Dissertations
In this dissertation we investigate self-distributive algebraic structures and their cohomologies, and study their relation to topological problems in knot theory. Self-distributivity is known to be a set-theoretic version of the Yang-Baxter equation (corresponding to Reidemeister move III) and is therefore suitable for producing invariants of knots and knotted surfaces. We explore three different instances of this situation. The main results of this dissertation can be, very concisely, described as follows. We introduce a cohomology theory of topological quandles and determine a class of topological quandles for which the cohomology can be computed, at least in principle, by means of …