Digital Shy Mapsmath.GT
Study shy maps in digital topology.
problem Properties of shy maps in digital topology.
method Study properties of shy maps.
result Properties of shy maps in digital topology.
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arXiv research
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.
169,341 papers · 148 categories
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48 results for “Topological Mapping”
New class of maps restricts manifolds strongly in algebraic topology.
problem Restricting manifolds in algebraic topology.
method Proposed a class of generalized special generic maps.
result Extended fundamental results on structures and algebraic topological properties.
This paper constructs real algebraic maps that are topologically special generic maps.
problem Constructing smooth maps in differential topology and real algebraic geometry.
method Constructs real algebraic maps that are topologically special generic maps.
result Real algebraic maps are topologically special generic maps.
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…
Topological normal generation proved for mapping class groups of certain surfaces.
problem Proving topological normal generation for mapping class groups of surfaces.
method Analyzing the end space of surfaces and using topological normal closure properties.
result Topological normal generation is equivalent to uniquely self-similar for surfaces with countable end space.
Bijective proof of map enumeration recursion formulae.
problem Counting maps of arbitrary topology.
method Iterating Tutte's algorithm and pair-of-pants decomposition.
result Combinatorial meaning for all terms of topological recursion.
Computes mapping class groups of 4-manifolds with boundary.
problem Computing mapping class groups for 4-manifolds with boundary.
method Topological and smooth methods applied to compact, simply connected 4-manifolds.
result Description of topological and stable smooth mapping class groups.
Authors create non-isometric 3-orbifolds with identical topology and volume.
problem Finding non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
method Constructing pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
result Demonstrated the existence of non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
Stability of mapping spaces is shown to be related to the D-topology.
problem Understanding the relationship between stability and the D-topology of mapping spaces.
method Reformulation and proof of stability theorems in diffeological étale manifolds.
result Stable classes of mapping spaces are D-open.
Images of maps from to math.AG
The study examines the topology of map germs and their images.
problem Understanding the topology of map germs and their images.
method Using the topology of the link to analyze the normal and non-normal images.
result Normal images of map germs are quotient singularities.
Study numerical invariants under retraction maps between topological spaces.
problem Understand behavior of invariants like cohomological dimensions under retractions.
method Introduced a notion of retraction and studied several numerical invariants.
result Proved inequalities between invariants hold under retractions.
This thesis introduces big mapping class groups and their structure.
problem Understanding mapping class groups of infinite-type surfaces.
method Systematic introduction and analysis of structure and topological generation.
result Key differences from finite-type mapping class groups.
Study on minimal torsion topological generators for mapping class groups of infinite-type surfaces.
problem Minimal topological generating sets of mapping class groups consisting of torsion elements.
method Investigation of minimal topological generating sets for consisting entirely of torsion elements, with special attention to involutions.
result Minimal topological generating sets for consisting of torsion elements are found for various .
This paper characterizes stable polynomial mappings in a specific set.
problem Characterizing stable polynomial mappings in a given set.
method Analyzing polynomial mappings with specific degrees and determining topological equivalence.
result Effective determination of mappings with generic topology.
Study the periods mapping from hyperelliptic curves, revealing fiber topology.
problem Global topology of 2D fibers of the periods mapping.
method Decomposition of moduli space into polyhedra labeled by planar graphs.
result Investigation of low dimensional fibers of the periods mapping.
Overview of infinite surface mapping class groups.
problem Understanding mapping class groups of infinite surfaces.
method Survey of recent research findings.
result Recent developments in mapping class groups of infinite surfaces.
We investigate how Viro's integral calculus applies for the study of the topology of stable maps. We also discuss several applications to Morin maps and complex maps.
Shy Maps in Topologymath.GT
Shy maps preserve path-connectedness in continuous functions.
problem Understanding properties of continuous functions in topological spaces.
method Defining shy maps as continuous functions with specific path-connected inverse images.
result Every shy map onto a semilocally simply connected space induces a surjection of fundamental groups.
Study bounds topological entropy of maps on surfaces with punctures based on mapping torus homology.
problem Relating topological entropy of pseudo-Anosov maps to homology of mapping tori.
method Analyzing the topological entropy of pseudo-Anosov maps on surfaces with punctures and relating it to the rank of the first homology of their mapping tori.
result Entropy of a pseudo-Anosov map is bounded by a formula involving the genus, number of punctures, and homology rank.
New EZ-structure maps mapping class group actions.
problem Mapping class group actions on surfaces.
method Constructing a boundary with minimal, strongly proximal, and topologically free action.
result Boundary acts on mapping class group with desired properties.
On Hölder regularity of the singular set of energy minimizing harmonic maps into closed manifoldsmath.AP
Proves part of the singular set of energy minimizing harmonic maps is a topological manifold.
problem Characterizing the singular set of energy minimizing harmonic maps.
method Analyzes topological and analytic properties of tangent maps.
result Proves part of the singular set is a topological manifold.
The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …
Involutions generate mapping class groups of infinite surfaces.
problem Generating involutions for mapping class groups of infinite surfaces.
method Analyzing infinite surfaces with n ends, showing involutions generate groups for n ≥ 6 and n ≥ 3.
result Involutions generate mapping class groups for n ≥ 6 and n ≥ 3.
Study topological quantum mechanics on orbifolds with geometric interpretation.
problem Quantum mechanical models on symplectic orbifolds.
method Explicit orbifold version of quantum HKR map and exact semi-classical approximation.
result Geometric and quantum field theoretic interpretation of orbifold algebraic index.
This paper finds minimal sets of generators for mapping class groups of specific surfaces.
problem Finding minimal sets of generators for mapping class groups of infinite-type surfaces.
method Analyzing specific surfaces to determine minimal sets of generators.
result Minimal sets of generators for are identified for (3 elements), (4 elements), and (2 elements).
The rho map preserves structure groups for high-dimensional manifolds.
problem Understanding the structure of high-dimensional manifolds.
method Proving the rho map is a homomorphism on the topological structure set.
result The rho map preserves the structure of topological manifolds.
New method uncovers global topology through local interactions, reducing algorithm complexity.
problem Global interaction is necessary for forming feature maps that preserve global topology.
method Competing agents engage in local interactions to form feature maps without global interaction.
result Local interactions can uncover global topology, leading to consistent map quality across diverse datasets.
Combining classical and modern topology, shows maps between certain manifolds must have degree zero.
problem Degree zero maps between certain manifolds
method Combining Thom's work on the Steenrod problem with simplicial volume, using Thom spaces and Steenrod powers
result Every map between certain manifolds must have degree zero
Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
problem Embedding maps in higher dimensions without self-intersections.
method Lifting maps to embeddings in product spaces.
result Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
Topology on mapping class group leads to generic results on surface properties.
problem Defining and analyzing a topology on mapping class groups.
method Introduced a twist-cofinite topology on mapping class groups of surfaces.
result Generic properties of subsets, such as pseudo-Anosov maps and Heegaard manifolds.
Study approximates top Lyapunov exponents for surface mapping classes.
problem Approximating topological Lyapunov exponents for surface mapping classes.
method Periodic approximation and joint spectral radius extension.
result Top Lyapunov exponents can be approximated by periodic orbits.
The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional Topology, Trieste Italy 2001
The study restricts manifolds with certain explicit SGL maps and constructs them.
problem Restrictions on manifolds admitting specific SGL maps.
method Generalization of Morse functions and canonical projections to construct SGL maps.
result Manifolds admitting certain explicit SGL maps are strongly topologically restricted.
The study finds topological barriers for robustly transitive maps on surfaces.
problem Identifying necessary conditions for robustly transitive maps on surfaces.
method Analyzing partial hyperbolicity and homotopy to linear maps.
result Robustly transitive maps on surfaces are limited to torus and klein bottle, and homotopic to linear maps with eigenvalues > 1.
The bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a hyperbolic 3-manifold with boundary to its bending measured geodesic lamination. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the s…
We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological vector spaces to Banach spaces.
Maps with boundary definite fold points restrict manifold structure.
problem Restricting the global structure of manifolds with boundary.
method Introducing boundary special generic maps and deriving differential-topological restrictions.
result New results on non-singular extensions of special generic maps.
Assembly maps study topological cyclic homology of group algebras at primes.
problem Study topological cyclic homology of group algebras at primes.
method Use assembly maps to analyze for various groups.
result Proves various properties of assembly maps for different groups.
The paper studies harmonic map flow and its singularities, proving global solutions and no-loss-of-topology.
problem Analyzing and resolving singularities in harmonic map flow.
method Analysis of finite-time singularities and a canonical way to flow beyond them.
result Proves global solutions and no-loss-of-topology for arbitrary maps.
The paper explores mapping class groups and their quantum field theory representations.
problem Understanding finite dimensional representations of mapping class groups.
method Survey of topological quantum field theory aspects.
result Discussion of finite dimensional representations in quantum field theory.
We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other and is invariant by topological conjugacies that preserve orientation. We prove…
In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a topologically excisive functor, and for coarse topological spaces there is an ass…
Random walks on mapping class groups have topological entropy that matches drift.
problem Understanding the topological entropy of random walks on mapping class groups.
method Defined topological entropy and proved it almost surely matches drift.
result Topological entropy of random walks on mapping class groups almost surely equals drift.
Uniformizing maps and period maps are topologically tame, leading to algebraicity of Hodge loci.
problem Understanding the algebraicity of Hodge loci in arithmetic quotients.
method Proving topological tameness of uniformizing maps and period maps, applying Peterzil-Starchenko's o-minimal GAGA theorem.
result The Hodge locus of is a countable union of algebraic subvarieties of .
The paper examines real analytic map germs and their topology, focusing on Lê-Milnor fibrations.
problem Analyzing the topology of real analytic map germs with isolated critical values.
method Comparing the topology of with compositions of projections and providing conditions for Lê-Milnor fibrations.
result Necessary and sufficient conditions for a Lê-Milnor fibration in the tube.
Study cohomology rings of 3D manifolds with round fold maps into the plane.
problem Understanding cohomology rings of 3D manifolds with round fold maps.
method Analyzing cohomology rings of 3D manifolds admitting round fold maps into the plane.
result Explicit new study showing relation between coefficient rings and topological types of round fold maps.
Study mapping class group actions on infinite-type surfaces.
problem When does the mapping class group of an infinite-type surface act on a graph with unbounded orbits?
method Introduced a topological invariant to determine the existence of such actions.
result Many big mapping class groups have nontrivial coarse geometry.
The Banach manifold math.DG
Smooth maps between manifolds form a Banach manifold.
problem Understanding the structure of maps between manifolds.
method Detailed rigorous proof of the smooth manifold structure.
result The set of times continuously differentiable maps between manifolds forms a smooth Banach manifold.