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.
Smooth contact maps are always smooth in rigid Carnot groups.
The study extends calibrated geometry to smooth maps and finds energy bounds.
Abstract reviews geometric theories of smooth and F-smooth systems.
A Reeb space is defined as the space of all the connected components of inverse images of a smooth map, which is a fundamental tool in studying smooth manifolds using generic smooth maps whose codimensions are not positive such as Morse functions, their higher dimensional versions including fold maps and general stable…
This paper constructs real algebraic maps that are topologically special generic maps.
Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
Variant of previous work on smooth algebraic functions with compact and non-compact preimages.
We show that every smooth manifold admits a smooth triangulation transverse to a given smooth map. This removes the properness assumption on the smooth map used in an essential way in Scharlemann's construction [5].
Computes mapping class groups of 4-manifolds with boundary.
Paper studies smoothness of bi-conformal heat flow on 4-manifolds.
Adapts a short argument to derive a stability theorem for smooth maps.
Defines manifolds of mappings between function spaces and discusses their properties.
In this paper we study fundamental properties of geodesic mappings with respect to the smoothness class of metrics. We show that geodesic mappings preserve the smoothness class of metrics. We study geodesic mappings of Einstein spaces.
Smooth maps show Gromoll filtration for spheres.
Abstracts a theorem for non-smooth maps in infinite dimensions.
Smooth contact mappings in a flat (2,3,5)-distribution are shown to be smoother.
The paper studies branched surfaces and their properties.
The paper extends properties of smooth functions to closed sets and maps.
Survey on harmonic maps in non-smooth spaces, focusing on rigidity.
The paper explores different smooth map notions on convex sets and their relationships.
The paper proves a smooth Birman-Hilden theorem for hyperkähler manifolds.
Geometric cohomology model uses co-oriented maps to define a product structure.
Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of smoothly local properties. In realising the definition of a local property at a pa…
We give several versions of local and global inverse mapping theorem for tame non necessarily smooth, mappings. Here tame mapping means a mapping which is subanalytic or, more generally, definable in some o-minimal structure. Our sufficient conditions are formulated in terms of various properties (convexity, positivity…
In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes special generic maps on spheres and such maps have been constructed on smooth bundles …
Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…
We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group to smooth maps into a homogeneous space , and determine the global monodromy obstruction to reconstructing such maps from infinitesimal data. The logarithmic derivative of the embedding of a submanifold $Σ\subset M…
Smooth maps bound Betti numbers of zero sets.
Proves a Thom Isotopy Theorem for nonproper semialgebraic maps.
This is an overview article. After an introduction to convenient calculus in infinite dimensions, the foundational material for manifolds of mappings is presented. The central character is the smooth convenient manifold of all smooth mappings from a finite dimensional Whitney manifold germ into a …
Study smooth mappings between manifolds and their properties.
A smooth map between smooth manifolds is called a special generic map if it has only definite fold points as its singularities. In this paper, we give conditions for a special generic map into the 3-dimensional Euclidean space to be factored as the composition of an embedding and a projection for certain dimensions.
We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between …
In this paper we extend Y.Eliashberg's -principle to arbitrary generic smooth maps of smooth manifolds. Namely, we prove a necessary and sufficient condition for a continuous map of smooth manifolds of the same dimension to be homotopic to a generic map with a prescribed Thom-Boardman singularity at each point…
We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds admit a unique differential, coinciding with the usual one. Thus smooth manifolds fo…
Proves rigidity of maps between manifolds with scalar curvature constraints.
Consider the equivariant wave map equation from Minkowski space to a rotationnally symmetric manifold which has an equator (example: the sphere). In dimension 3, this article gives a necessary and sufficient condition for the existence of a smooth self-similar blow up profile. More generally, we study the relation betw…
Study on manifolds that map to lower dimensions with specific critical points.
Smooth maps preserve distances on specific revolution surfaces.
The paper simplifies smooth maps to spheres and planes, showing homotopy and embedding properties.
We present a definable smooth version of the Thom transversality theorem. We show further that the set of non-transverse definable smooth maps is nowhere dense in the definable smooth topology. Finally, we prove a definable version of a theorem of Trotman which says that the Whitney -regularity of a stratification…
The paper generalizes a result on smooth mapping class groups and proves a property of Dehn twists in 4-manifolds.
Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f: O -> P between smooth orbifolds O and P. We show that Sard's theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence o…
Maps with many singularities found in complex space.
Residually finite groups found in manifold automorphisms.
Study differential operators over maps and their applications in supermanifolds.
Constructs real algebraic maps with specific geometric constraints.
Let be a smooth area decreasing map between two Riemannian manifolds $(M,\gm)$ and $(N,\gn)$. Under weak and natural assumptions on the curvatures of $(M,\gm)$ and $(N,\gn)$, we prove that the mean curvature flow provides a smooth homotopy of to a constant map.