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.
This paper constructs real algebraic maps that are topologically special generic maps.
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…
The study extends calibrated geometry to smooth maps and finds energy bounds.
Smooth maps show Gromoll filtration for spheres.
Abstracts a theorem for non-smooth maps in infinite dimensions.
Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
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.
The paper studies branched surfaces and their properties.
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 …
Defines manifolds of mappings between function spaces and discusses their properties.
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…
Smooth contact maps are always smooth in rigid Carnot groups.
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…
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…
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…
Survey on harmonic maps in non-smooth spaces, focusing on rigidity.
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 …
The paper proves a smooth Birman-Hilden theorem for hyperkähler manifolds.
We give some general criteria of being a homeomorphism for continuous mappings of topological manifolds, as well as criteria of being a diffeomorphism for smooth mappings of smooth manifolds. As an illustration, we apply these criteria to the problems arising in two- and three-dimensional grid generation.
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…
The paper simplifies smooth maps to spheres and planes, showing homotopy and embedding properties.
The author studies regions foliated by 1D families of functions and their applications.
Smooth maps bound Betti numbers of zero sets.
The paper generalizes a result on smooth mapping class groups and proves a property of Dehn twists in 4-manifolds.
In this article, we introduce an analogous problem to Yamabe type problem considered by Case, J., which generalizes the Escobar-Riemann mapping problem for smooth metric measure spaces with boundary. The last problem will be called Escobar-Riemann mapping type problem. For this purpose, we consider the generalization o…
Generalizes Lefschetz fibrations with rational homology disk smoothings.
Generalized Stacey-Roberts lemma for Banach manifolds.
Abstract reviews geometric theories of smooth and F-smooth systems.
Research explores real algebraic realization of round fold maps of codimension -1.
The paper examines rational homology spheres that admit special generic maps into Euclidean spaces.
We extend Y.Eliashberg's -principle to smooth maps of surfaces which are allowed to have cusp singularities, as well as folds. More precisely, we prove a necessary and sufficient condition for a given map of surfaces to be homotopic to one with given loci of folds and cusps. Then we use these results to obtain a nec…
The paper shows how to approximate continuous maps to smooth CW complexes.
Variant of previous work on smooth algebraic functions with compact and non-compact preimages.
Fold maps are higher dimensional versions of Morse functions, which play important roles in the studies of smooth manifolds, and such general maps also have been fundamental tools in the studies of smooth manifolds by using generic maps. In this paper, we study {\it simple} fold maps, which are fold maps such that any …
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].
Isothermic nets created from special maps for smooth surfaces.
New methods decompose manifolds into submanifolds via fold maps.
Constructs real algebraic maps with specific geometric constraints.
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.
Generators of the 4-sphere's smooth mapping class group via diffeomorphisms of Montesinos twins.
Unified proof of smooth fibration theorems for collapsed manifolds.
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.
New algorithm estimates transport maps with nearly optimal error.
Boundary Dehn twists become trivial after abelianization.
We discuss generic smooth maps from smooth manifolds to smooth surfaces, which we call "Morse 2-functions", and homotopies between such maps. The two central issues are to keep the fibers connected, in which case the Morse 2-function is "fiber-connected", and to avoid local extrema over 1-dimensional submanifolds of th…