Related papers: Index and secondary index theory for flat bundles …
This article develops a duality principle for a semi-linear model in micro-magnetism. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation…
We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
This is a very brief survey of some results in the geometry of string duality delivered at a lecture given at ICM 1998, Berlin. String Duality is the statement that one kind of string theory compactified on one space is equivalent in some…
I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.
Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over…
This note gives a unifying characterization and exposition of strongly irreducible elements and their duals in lattices. The interest in the study of strong irreducibility stems from commutative ring theory, while the dual concept of strong…
This short communication develops a convex dual variational formulation for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The…
We verify that the formula of X. Ma for the analytic torsion form of an iterated fibration implies that Lott's secondary analytic index is functorial.
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We present the functor associated with a local algebra bundle and the differential structure of the double fibre bundle it produces when applied to a differential manifold.
The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix…
We prove a duality theorem applicable to a a wide range of specialisations, as well as to some generalisations, of tangles in graphs. It generalises the classical tangle duality theorem of Robertson and Seymour, which says that every graph…
It has been a long-standing problem to find an adequate definition of a Clifford index for higher rank vector bundles on curves, which should capture the complexity of the curve in its moduli space. An interesting proposal in rank 2 has…
Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend…
Recently it has been shown that the property of forward-flatness for discrete-time systems, which is a generalization of static feedback linearizability and a special case of a more general concept of flatness, can be checked by two…
We will show that the duality for regular weight systems introduced by K. Saito can be interpreted as the duality for orbifoldized Poincare polynomials.
This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive…
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.