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.
The paper bridges diffeological bundle theory with higher topos theory.
New pushforward operation on vector pseudo-bundles creates new examples.
Defines sheaves and Čech cohomology for diffeological spaces and classifies principal bundles.
Universal connection constructed using diffeology theory.
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 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…
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…
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…
Diffeology explores -forms and bundles with more information than traditional differential forms.
Study tiling spaces over irrational tori using diffeological classification.
Study non-formal pseudo-differential operators over formal ones.
Constructs diffeological moduli stacks for Higgs and flat bundles on Kähler manifolds
We define a diffeology on the Milnor classifying space of a diffeological group , constructed in a similar fashion to the topological version using an infinite join. Besides obtaining the expected classification theorem for smooth principal bundles, we prove the existence of a diffeological connection on any princip…
New method for foliated bundles using holonomy groupoids.
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 …
New Morita equivalence for diffeological groupoids defined.
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 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…
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…
Study on Čech-de Rham obstruction in diffeological spaces.
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…
New cohomology theory for diffeological spaces developed.
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.
New spherical Milnor spaces for diffeological groups with geometric and topological properties.
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…
New method recovers differential cohomology from diffeological spaces.
We prove that isomorphism classes of principal bundles over a diffeological space are in bijection to certain maps on its free loop space, both in a setup with and without connections on the bundles. The maps on the loop space are smooth and satisfy a "fusion" property with respect to triples of paths. Our bijections a…
We consider the notion of the De Rham operator on finite-dimensional diffeological spaces such that the diffeological counterpart Λ^1(X) of the cotangent bundle, the so-called pseudo-bundle of values of differential 1-forms, has bounded dimension. The operator is defined as the composition of the Levi-Civita connection…
Smooth structures on diffeological spaces and sheaves, resolving conjectures.
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…
New type of spaces with tangent structures for analysis.
Two de Rham complexes in diffeology are compared using a factor map.
The paper revisits a claim about a principal bundle over a contractible base and finds it non-trivial.
This manuscript attempts to present a way in which the classical construction of the Dirac operator can be carried over to the setting of diffeology. A more specific aim is to describe a procedure for gluing together two usual Dirac operators and to explain in what sense the result is again a Dirac operator. Since vers…
Abstract Lie algebroids generalize Lie algebroids to abstract categories.
Study homotopy sheaves on categories and their presheaves, proving descent properties.
The paper defines connections on Lie groupoid bundles and their properties.
In this paper, we start from an extension of the notion of holonomy on diffeological bundles, reformulate the notion of regular Lie group or Frölicher Lie groups, state an Ambrose-Singer theorem that enlarges the one stated in \cite{Ma2}, and conclude with a differential geometric treatment of KP hierarchy. The example…
Diffeology extends differential geometry to complex spaces.
This paper generalizes optimization techniques to diffeological spaces.
This paper adapts submersions, immersions, and étale maps to diffeology.
Analyzes geometric structures on profinite diffeological spaces.
Introduces a new framework for Riemannian diffeology.
This work establishes properties on diffeological structures for set-valued maps and measures.
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…
We consider orbifolds as diffeological spaces. This gives rise to a natural notion of differentiable maps between orbifolds, making them into a subcategory of diffeology. We prove that the diffeological approach to orbifolds is equivalent to Satake's notion of a V-manifold and to Haefliger's notion of an orbifold. This…
New bridge between diffeology and noncommutative geometry.