Related papers: Triposes as a Generalization of Localic Geometric …
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
In this paper, we give an accessible introduction to the theory of orbispaces via groupoids. We define a certain class of topological groupoids, which we call orbigroupoids. Each orbigroupoid represents an orbispace, but just as with…
The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.
We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.
In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved.…
We define arroids as an abstract axiom set encoding the intersection properties of arrangements of curves. The tropicalization of the complement of arrangement of curves meeting pairwise transversely is shown to be determined by the…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…
The classifying topos of a geometric theory is a topos such that geometric morphisms into it correspond to models of that theory. We study classifying toposes for different infinitary logics: first-order, sub-first-order (i.e. geometric…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
In this paper we present an introduction to morphological calculus in which geometrical objects play the rule of generalised natural numbers.
In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence…
We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases…
In this expository article, we explain how to use localization to compute Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten invariants of smooth toric Deligne-Mumford stacks.
Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.
We study toposes satisfying De Morgan's law, in particular we give characterizations of geometric theories whose classifying topos is De Morgan, clarifying the link with the amalgamation property of the category of models of such theory. We…
In this paper, we extend the formal definition of topological surgery by introducing new notions in order to model natural phenomena exhibiting it. On the one hand, the common features of the presented natural processes are captured by our…
Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…