Related papers: Coherence simplices
Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a…
Call a pure Hodge structure geometric if it is contained in the cohomology of a smooth complex projective variety. The main goal is to show that for any set of Hodge numbers (subject to the obvious constraints), there exists a geometric…
Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this article, we introduce the notion of L-fuzzy simplicial homology, a…
We give a short topological proof of coherence for categorified non-symmetric operads by using the fact that the diagrams involved form the 1-skeleton of simply connected CW complexes. We also obtain a "one-step" topological proof of Mac…
We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply connected cohomogeneity one topological…
We introduce and study configuration schemes, which are obtained by ``glueing'' usual schemes along closed embeddings. The category of coherent sheaves on a configuration scheme is investigated. Smooth configuration schemes provide…
It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be…
We construct a system of coherent states for the hydrogen atom that is expressed in terms of elementary functions. Unlike to the previous attempts in this direction, this system possesses the properties equivalent to the most of those for…
Simplicial homology manifolds are proposed as an interesting class of geometric objects, more general than topological manifolds but still quite tractable, in which questions about the microstructure of space-time can be naturally…
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative…
To a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on…
Let $A$ be either a simplicial complex $K$ or a small category $\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \delta\colon…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration…
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from…
Preservation of coherence is a fundamental yet subtle phenomenon in open systems. We uncover its relation to symmetries respected by the system Hamiltonian and its coupling to the environment. We discriminate between local and global…
Both the intensity distribution and the degree of coherence between pairs of points along the propagation axis (z-coherence) are derived in closed form for a phenomenon of self-focusing produced by circularly coherent light. The first…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…