Related papers: Fiberwise Intersection Theory
Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of…
It is proved that one can choose a control function on an arbitrary small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number…
We define a $\mathbb{Z}_2$-valued invariant for transversely-intersecting coassociative $4$-folds equipped with spin structures. Our main result shows this invariant provides an obstruction to separating two such coassociatives through a…
We use the notion of isomorphism between two invariant vector fields to shed new light on the issue of linearization of an invariant vector field near a relative equilibrium. We argue that the notion is useful in understanding the passage…
Logarithmic representations of the bordism category are considered as a framework for capturing a class of additive invariants characterising Reidemeister torsions.
Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced…
We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as…
This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, the intersection index of algebraic varieties, and the notion of orientability of vector bundles. The novel approach adopted in it…
We show that there are obstructions to the existence of certain types of invariant subspaces of the Milnor monodromy; this places restrictions on the cohomology of Milnor fibres of non-isolated hypersurface singularities.
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \sigma-finite morphism between difference curves are…
We introduce an equivalence relation, called cobordism, for words and study cobordism invariants of words inspired by methods of low-dimensional topology.
Binary decision theory has been applied to the general interferometric problem. Optimal detection scheme-according to the Neyman-Pearson criterion-has been considered for different phase-enhanced states of radiation field, and the…
We propose a theory of contact invariants and open string invariants, assuming that the almost complex $J$ is either non-degenerate or of Bott-type. We do not choose the complex structure $\tilde{J}$ such that $L_X\tilde{J}=0$ on periodic…
We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.
Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…
Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.
We consider birack and switch colorings of braids. We define a switch structure on the set of permutation representations of the braid group and consider when such a representation is a switch automorphism. We define quiver-valued…
An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of non-repeating Whitney towers. The accompanying higher-order intersection…
We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a…
In this paper, we develop the general intersection theory of nef b-divisors, extending the movable intersection theory. We define a notion of restricted volume of b-divisors and prove a quantitative version of the monotonicity of the…