Related papers: Unimodularity unified
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and…
Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to moduli spaces of submanifolds of higher…
Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and…
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all groupoid structure maps are continuous. The notion of…
This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type with nodes of another type, according to the…
We begin the process of classifying all supersymmetric theories with quantum modified moduli. We determine all theories based on a single SU or Sp gauge group with quantum modified moduli. By flowing among theories we have calculated the…
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissibility for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…
The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations…
We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…
We generalize the notion of a modified trace (or m-trace) to the setting of non-unimodular categories. M-traces are known to play an important role in low-dimensional topology and representation theory, as well as in studying the category…