A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New pushforward operation on vector pseudo-bundles creates new examples.
Finite spaces can be or not coproducts of subspaces.
This paper aims to describe the behavior of diffeological differential forms under the operation of gluing of diffeological spaces along a smooth map. In the diffeological context, two ways of looking at diffeological forms are available, that of the vector space of all diffeological forms on a given space, and that of…
We consider one possible definition of a diffeological connection on a diffeological vector pseudo-bundle. It is different from the one proposed in [7] and is in fact simpler, since it is obtained by a straightforward adaption of the standard definition of a connection as an operator on the space of all smooth sections…
It is known that the only finite-dimensional diffeological vector space that admits a diffeologically smooth scalar product is the standard space of appropriate dimension. In this note we consider a way to circumnavigate this issue, by introducing a notion of pseudo-metric, which, said informally, is the least-degenera…
This paper deals with some basic constructions of linear and multilinear algebra on finite-dimensional diffeological vector spaces. We consider the diffeological dual formally checking that the assignment to each space of its dual defines a covariant functor from the category of finite-dimensional diffeological vector …
We consider the diffeological version of the Clifford algebra of a (diffeological) finite-dimensional vector space; we start by commenting on the notion of a diffeological algebra (which is the expected analogue of the usual one) and that of a diffeological module (also an expected counterpart of the usual notion). Aft…
We study the relationship between many natural conditions that one can put on a diffeological vector space: being fine or projective, having enough smooth (or smooth linear) functionals to separate points, having a diffeology determined by the smooth linear functionals, having fine finite-dimensional subspaces, and hav…
New cohomology theory for diffeological spaces developed.
We consider a diffeological counterpart of the notion of a vector bundle (we call this counterpart a pseudo-bundle, although in the other works it is called differently; among the existing terms there are a "regular vector bundle" of Vincent and "diffeological vector space over X" of Christensen-Wu). The main differenc…
Diffeological and differential spaces are generalisations of smooth structures on manifolds. We show that the "intersection" of these two categories is isomorphic to Frölicher spaces, another generalisation of smooth structures. We then give examples of such spaces, as well as examples of diffeological and differential…
We show that a diffeological bundle gives rise to an exact sequence of internal tangent spaces. We then introduce two new classes of diffeological spaces, which we call weakly filtered and filtered diffeological spaces, whose tangent spaces are easier to understand. These are the diffeological spaces whose categories o…
New type of spaces with tangent structures for analysis.
Study of generalized vector bundles and their geometric tools.
We study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces and infinite-dimensional spaces. We focus on two definitions. The internal tangent space of a diffeological space is defined using smooth cur…
We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.
Diffeology explores -forms and bundles with more information than traditional differential forms.
Lie algebras of quotient groups defined under specific conditions.
Smooth structures on infinite dimensional Grassmannians and non-commutative cross-ratios.
We develop the theory of smooth principal bundles for a smooth group , using the framework of diffeological spaces. After giving new examples showing why arbitrary principal bundles cannot be classified, we define -numerable bundles, the smooth analogs of numerable bundles from topology, and prove that pulling ba…
Although our main interest here is developing an appropriate analog, for diffeological vector pseudo-bundles, of a Riemannian metric, a significant portion is dedicated to continued study of the gluing operation for pseudo-bundles introduced in arXiv:1509.03023. We give more details regarding the behavior of this opera…
This paper generalizes optimization techniques to diffeological spaces.
The paper bridges diffeological bundle theory with higher topos theory.
Study tiling spaces over irrational tori using diffeological classification.
Diffeology extends differential geometry to complex spaces.
A diffeological connection on a diffeological vector pseudo-bundle is defined just the usual one on a smooth vector bundle; this is possible to do, because there is a standard diffeological counterpart of the cotangent bundle. On the other hand, there is not yet a standard theory of tangent bundles, although there are …
Analyzes geometric structures on profinite diffeological spaces.
Defines sheaves and Čech cohomology for diffeological spaces and classifies principal bundles.
Introduces a new framework for Riemannian diffeology.
We consider the diffeological pseudo-bundles of exterior algebras, and the Clifford action of the corresponding Clifford algebras, associated to a given finite-dimensional and locally trivial diffeological vector pseudo-bundle, as well as the behavior of the former three constructions (exterior algebra, Clifford action…
New derivations on diffeological spaces are not smooth, expanding tangent space definitions.
We study diffeologies on locally convex spaces and their application to smooth multiplication of distributions.
Paper constructs infinitely many tangent functors on diffeological spaces.
The original de Rham cohomology due to Souriau and the singular cohomology in diffeology are not isomorphic to each other in general. This manuscript introduces a singular de Rham complex endowed with an integration map into the singular cochain complex which gives the de Rham theorem for every diffeological space. It …
A new method for optimization in diffeological spaces using linearizations.
Study on diffeologies on locally convex spaces and smooth multiplication of distributions.
This paper adapts submersions, immersions, and étale maps to diffeology.
Proves Mayer-Vietoris sequence for diffeological spaces using generating families.
Study of tangent spaces in diffeological spaces under Lie group actions.
Introduces a framework for rational homotopy theory in diffeological spaces.
Diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces. For each diffeological space, Iglesias-Zemmour introduced a natural topology called the -topology. However, the -topology has not yet been studied seriously in the existing literature. In this paper, we…
Quasifold groupoids and diffeological quasifolds are studied, showing an equivalence of categories.
We consider certain groups of tree automorphisms as so-called diffeological groups. The notion of diffeology, due to Souriau, allows to endow non-manifold topological spaces, such as regular trees that we look at, with a kind of a differentiable structure that in many ways is close to that of a smooth manifold; a suita…
Diffeologies unify infinite-dimensional geometry and PDEs, enhancing classical function spaces.
Riemannian metrics on orbifolds are equivalent to diffeological ones.
Study on Čech-de Rham obstruction in diffeological spaces.
Stability of mapping spaces is shown to be related to the D-topology.
In this paper, we consider diffeological spaces as stacks over the site of smooth manifolds, as well as the "underlying" diffeological space of any stack. More precisely, we consider diffeological spaces as so-called concrete sheaves and show that the Grothendieck construction sending these sheaves to stacks has a left…