Proof shows homeomorphism problem is unsolvable.
problem Unsolvable homeomorphism problem in topology.
method Detailed proof of Markov's theorem.
result Existence of unrecognizable manifolds in higher dimensions.
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48 results for “homeomorphism problem”
The study of periodic subgroups in homeomorphism groups of manifolds.
problem Burnside problem for homeomorphism groups of manifolds.
method Analyzing surface and circle homeomorphism groups, extending Tits alternative.
result Every finitely generated periodic subgroup is finite for most manifolds.
We give a more geometric approach to an algorithm for deciding whether two hyperbolic 3-manifolds are homeomorphic. We also give a more algebraic approach to the homeomorphism problem for geometric, but non-hyperbolic, 3-manifolds.
No algorithm exists to decide 4-manifold homeomorphism.
problem Deciding homeomorphism for 4-manifolds.
method Demonstrated through a specific example of a connected sum of 12 copies of S^2 × S^2.
result No algorithm exists for deciding homeomorphism of 4-manifolds.
Algorithm decides if two hyperbolic 3-manifolds are homeomorphic.
problem Determining if two hyperbolic 3-manifolds are homeomorphic.
method Algorithm finds hyperbolic structures and compares geometric manifolds.
result Algorithm runs in bounded time for triangulations with at most tetrahedra.
Uniform first order interpretation of the second order theory of countable groups of homeomorphismsmath.GR
Uniform interpretation of group theory in manifold homeomorphisms.
problem Understanding group properties in manifold homeomorphisms.
method First order theory interpretation of second order group theory.
result Many group theory problems encoded in homeomorphism groups.
Homeomorphisms of hyperbolic 3-manifolds have invariant sets under certain conditions.
problem Understanding invariant sets for homeomorphisms on hyperbolic 3-manifolds.
method Shadowing techniques and analysis of invariant sets under positive speed with respect to a uniform foliation.
result Homeomorphisms of hyperbolic 3-manifolds are forced to have invariant sets, preventing them from being minimal.
We solve the isomorphism problem for the whole class of Lins-Mandel gems (graphs encoded manifolds). We also present certain homeomorphisms of branched cyclic coverings of two-bridge hyperbolic links. As a consequence, we prove that, in in a wide subset of interesting cases, the isomorphism conditions for Lins-Mandel g…
The pure braid group cannot be realized as area-preserving homeomorphisms.
problem Realizing the pure braid group inside area-preserving homeomorphisms.
method Using rotation numbers to show non-realizability.
result The pure braid group has no realization inside area-preserving homeomorphisms.
We introduce a new class of possibly noncompact n-dimensional manifolds without boundary associated to finite data which we call topological automata. This class is large enough to contain many interesting examples of open 2-dimensional and 3-dimensional manifolds of interest to low-dimensional topologists. Our main re…
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.
Proves common stellar subdivisions for all PL homeomorphic polyhedra.
problem Proving common stellar subdivisions for all PL homeomorphic polyhedra.
method Proved weighted strong factorization conjecture and iterated blowups.
result Every two PL homeomorphic polyhedra have a common stellar subdivision.
The paper classifies 4-manifolds with given boundaries.
problem Extending homotopy equivalences of boundaries to 4-manifolds.
method Surgery theory and classification of groups.
result Conditions for extending homotopy equivalences to homeomorphisms.
Extends Palais' result on diffeomorphisms to homeomorphisms and bi-Lipschitz mappings.
problem Extending diffeomorphisms to global mappings of manifolds.
method Elementary argument for diffeomorphisms, deep results for homeomorphisms and bi-Lipschitz mappings.
result Extension of Palais' result to homeomorphisms and bi-Lipschitz mappings.
Study on homeomorphism groups of manifolds using set theory.
problem Relationship between set theory and homeomorphism groups of manifolds.
method First-order rigidity, type versus conjugacy, axiom of constructibility, projective determinacy.
result Under V=L, homeomorphism groups of manifolds are first-order rigid and conjugacy class is determined by type.
The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a -manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case of diffeomorphisms. The theorem is a starting point for computing $H_1(\mathcal…
New proof associates partitions to isotopic pseudo-Anosov homeomorphisms.
problem Stable and unstable foliations for pseudo-Anosov homeomorphisms.
method Geometric realization of Fathi's result for isotopic homeomorphisms.
result Associated stable and unstable partitions for isotopic pseudo-Anosov homeomorphisms.
The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group action (Kechris-Solecki). It is shown that this result extends to locally compact …
Proves existence of sentences to identify homeomorphic manifolds.
problem Identifying homeomorphic manifolds using group properties.
method Defines sentences in group language to match homeomorphic manifolds.
result Existence of sentences to distinguish homeomorphic manifolds.
Global invertibility proven for orientation-preserving maps without homeomorphic extension.
problem Global invertibility of orientation-preserving Sobolev maps.
method Avoiding homeomorphic extension, study of strictly orientation-preserving maps.
result Global invertibility can be achieved without homeomorphic extension.
New homeomorphism found in Klein bottle group.
problem Understanding homeomorphisms of Klein bottle.
method Using recent results on commutator length.
result Existence of homeomorphism with positive stable commutator length.
Study weak conjugacy in surface homeomorphisms.
problem Understanding weak conjugacy in homeomorphisms of surfaces.
method Exploring the group of homeomorphisms isotopic to the identity.
result New insights into weak conjugacy relations.
Paper explains dynamics of homeomorphisms to mapping tori geometry.
problem Understanding dynamics of end-periodic homeomorphisms.
method Illustration-driven overview of recent results.
result Analogue of Brock's theorem for infinite-type surfaces.
Nielsen realization problem for the mapping class group asks whether the natural projection has a section. While all the previous results use torsion elements in an essential way, in this paper, we focus on the much more difficult problem of realization of…
In this paper we prove two results, one semi-historical and the other new. The semi-historical result, which goes back to Thurston and Riley, is that the geometrization theorem implies that there is an algorithm for the homeomorphism problem for closed, oriented, triangulated 3-manifolds. We give a self-contained proof…
For each odd integer r greater than one and not divisible by three we give explicit examples of infinite families of simply and tangentially homotopy equivalent but pairwise non-homeomorphic closed homogeneous spaces with fundamental group isomorphic to Z/r. As an application we construct the first examples of manifold…
Unified framework recovers and improves classical Brouwer homeomorphism results.
problem Classical Brouwer homeomorphism theory and its dynamics.
method Unified foliated framework combining Le Calvez's and Handel's methods.
result Recovery and improvement of classical results in Brouwer homeomorphism theory.
Every homeomorphism of Euclidean space is a commutator of two homeomorphisms.
problem Understanding the structure of homeomorphisms in Euclidean space.
method Proving every orientation-preserving homeomorphism can be written as a commutator of two such homeomorphisms.
result Every orientation-preserving homeomorphism of Euclidean space is a commutator of two homeomorphisms.
Adapts pivoting technique to circle homeomorphisms for proofs.
problem Probabilistic Tits alternative and exponential synchronization.
method Adapts Gou{ë}zel's pivoting technique.
result Different proofs of probabilistic Tits alternative and exponential synchronization.
Study covers of sphere with homeomorphisms lifting property.
problem Finite abelian covers of sphere with lifting homeomorphisms.
method Completely determined covers with specific lifting property.
result Properties of finite abelian covers with lifting homeomorphisms.
A multiobjective optimization problem is simplicial if the Pareto set and front are homeomorphic to a simplex and, under the homeomorphisms, each face of the simplex corresponds to the Pareto set and front of a subproblem. In this paper, we show that strongly convex problems are simplicial under a mild assumption on th…
In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link of the multiplicity problem with the famous Seifert conjecture (formulated in 1948) about multiple brake orbits for…
Goldman bracket distinguishes surface homeomorphisms.
problem Characterizing homeomorphisms between non-compact surfaces.
method Using the Goldman bracket to distinguish homeomorphisms.
result A homotopy equivalence is a homeomorphism if it preserves the Goldman bracket.
Study shows similar result to Margulis for Cantor set homeomorphisms.
problem Understanding groups of homeomorphisms of Cantor sets.
method Analogous to Margulis's proof for linear groups.
result Groups of homeomorphisms either preserve a measure or contain a free subgroup.
Positive factorization for pseudoperiodic homeomorphisms on surfaces.
problem Factorization of pseudoperiodic homeomorphisms on surfaces.
method Generalization of classical results on smooth germs of surfaces, topological characterization of monodromies, and use of positive factorization criteria.
result Pseudoperiodic homeomorphisms on surfaces with positive fractional Dehn twist coefficients and screw numbers admit a positive factorization.
We prove that the homeomorphism problem for 2-manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected -connectivity problem in graphs.
The study explores homeomorphism groups of self-similar 2-manifolds, including the 2-sphere and Cantor set.
problem Understanding the structure and properties of homeomorphism groups of self-similar 2-manifolds.
method Survey of recent results, exposition of classical results, treatment of stable sets, and proof of new theorems.
result Characterization of homeomorphisms of perfectly self-similar 2-manifolds and extensions of existing results.
New 4D homeomorphism shows surprising similarities to 2D.
problem Finding a 4D pseudo-Anosov homeomorphism.
method Building a specific example of a 5-manifold fibered over the circle.
result Compact 4-manifold with unique immersed and embedded surfaces.
Let X be a path-connected topological space admitting a universal cover. Let Homeo(X,a) denote the group of homeomorphisms of X preserving degree one cohomology class a. We investigate the distortion in Homeo(X,a). Let g be an element of Homeo(X,a). We define a Nielsen-type equivalence relation on the space of g-invari…
Study shows certain surface homeomorphisms groups can't be precompact.
problem Understanding precompactness of groups of surface homeomorphisms.
method Analyzing subgroup properties and transitivity of homeomorphisms.
result No subgroup of surface homeomorphisms can be Roelcke precompact.
We prove that the set of non-properness of a polynomial mapping of the three dimensional space which is a local homeomorphism cannot be homeomorphic to the real line
For each there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations `conjugated by '. We show that these families are free of relations, which determines the structure of `the group of homeomorphisms of finite type'. We also discuss a numbe…
Study classifies 2-manifolds with special homeomorphism groups.
problem Classifying 2-manifolds with specific homeomorphism groups.
method Introduced virtual Rokhlin property; classified homeomorphism groups of 2-manifolds.
result 2-manifolds with the virtual Rokhlin property have specific homeomorphism groups.
Study chaotic behavior in homeomorphism groups of countable products of spaces.
problem Investigate chaotic behavior in homeomorphism groups of countable products of various metrizable topological spaces.
method Construct numerous examples of chaotic groups of homeomorphisms of countable products of spaces.
result New chaotic groups of homeomorphisms of countable products of various metrizable topological spaces are discovered.
Extends continuity proof to non-compact manifolds and groups.
problem Automatic continuity for homeomorphism groups of non-compact manifolds.
method Proof extension to non-compact manifolds and groups.
result Homomorphisms from these groups to separable topological groups are continuous.
Generates special homeomorphisms for complex surfaces.
problem Creating specific homeomorphisms for infinite-type surfaces.
method General conditions for producing endperiodic loxodromics.
result Produces homeomorphisms acting loxodromically on arc graphs.
The study examines the realizability of a 4-manifold invariant for homeomorphisms.
problem Realizing the Casson-Sullivan invariant for homeomorphisms of 4-manifolds.
method Investigation of the invariant's realizability and application to surface isotopy.
result The invariant can be realized fully after stabilizing with a single for all orientable pairs of homeomorphic 4-manifolds.
Abstract: Lipschitz homeomorphisms are deformed using Perelman's methods.
problem Deformation of Lipschitz homeomorphisms
method Lipschitz analogues of Siebenmann's and Perelman's homeomorphism theory
result Lipschitz stability theorem and gluing theorem