Related papers: Structure theory of naturally reductive spaces
In this paper, we give a complete description of the deformation classes of real structures on minimal ruled surfaces. In particular, we show that these classes are determined by the topology of the real structure, which means that real…
We provide five rearticulations of the thesis that the structure of spacetime is conventional, rather than empirically determined, based upon variation of the structures that are empirically underdetermined and modal contexts in which this…
We study the interaction of structural subtyping with parametric polymorphism and recursively defined type constructors. Although structural subtyping is undecidable in this setting, we describe a notion of parametricity for type…
Every countable structure has a sentence of the infinitary logic $\mathcal{L}_{\omega_1 \omega}$ which characterizes that structure up to isomorphism among countable structures. Such a sentence is called a Scott sentence, and can be thought…
This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive $p$-adic group. The method of proof is to establish the presence of a very simple geometric…
Recently Stephen Theriault and I found an elementary construction of Anick's spaces and proved their main properties(arXiv:0710.1024).In this work the fundamental fibration is decomposed. This is useful in studying maps out of Anick's…
We introduce the notion of finitary computable reducibility on equivalence relations on the natural numbers. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular,…
In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.
Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of…
Conway's field No of surreal numbers comes both with a natural total order and an additional "simplicity relation" which is also a partial order. Considering No as a doubly ordered structure for these two orderings, an isomorphic copy of No…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which…
The backreaction of structure formation influences the cosmological evolution equation for the homogenous and isotropic average metric. In a cold dark matter universe this effect leads only to small corrections unless a substantial fraction…
Difference families are traditionally built using groups as their basis. This paper looks at what sort of generalised difference family constructions could be made, using the standard basis of translation and difference. The main result is…
Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.
We show how to construct the Hamiltonian structures of any reduction of the Benney chain (dKP) starting from the family of conformal maps associated to it.
Third-order ordinary differential equations with Lie symmetry algebras isomorphic to the nonsolvable algebra $\mathfrak{sl}(2,\mathbb{R})$ admit solvable structures. These solvable structures can be constructed by using the basis elements…