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This paper introduces categories of assemblies which are closely connected to realizability interpretations and which are based on an important subcategory of the effective topos. There is a list of properties which characterize these…
This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience. The objective of this paper is to help the reader feel…
In this paper we state some applications of Gr-category theory on the classification of crossed modules and on the classification of extensions of groups of the type of a crossed module.
The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for…
In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we give a rigorous derivation of the field equation recursion method in the abstract theory of…
We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification…
In this paper, we define the \textit{normal form} and \textit{normal coordinate} of a rational 3-tangle $T$ with respect to $\partial E_1$, where $E_1$ is the fixed two punctured disk in $\Sigma_{0,6}$. Among all normal coordinates of $T$…
This is the first part of a series on non-compact groups acting isometrically on compact Lorentz manifolds. This subject was recently investigated by many authors. In the present part we investigate the dynamics of affine, and especially…
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the reduction of the vector field and of the Poisson tensors. We show explicitly that, after the reduction on each one of the…
Real linear operators emerge in a range of mathematical physics applications. In this paper spectral questions of compact real linear operators are addressed. A Lomonosov-type invariant subspace theorem for antilinear compact operators is…
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
This is a survey paper of Shelah's pcf theory. In this part the theory is developed up to the pcf theorem.
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
We introduce toric complexes as polyhedral complexes consisting of rational cones together with a set of integral generators for each cone, and we define their associated face rings. Abstract simplicial complexes and rational fans can be…
Let J be the jacobian of a reduced projective curve C with nodes only. 1) We give a simple and natural definition for its many compactifications and show the connection with various other definitions appearing in the literature. 2) Among…
This is an introduction to small divisors problems. The material treated in this book was brought together for a PhD course I tought at the University of Pisa in the spring of 1999. Here is a Table of Contents: Part I One Dimensional Small…
We give bounds for the module sectional category of products of maps which generalise a theorem of Jessup for Lusternik-Schnirelmann category. We deduce also a proof of a Ganea type conjecture for topological complexity. This is a first…
Given a real, symmetric matrix S, we define the slice through S as being the connected component containing S of two orbits under conjugation: the first by the orthogonal group, and the second by the upper triangular group. We describe some…