Surface groups are uniquely identified by their profinite completions.
problem Identifying surface groups among limit groups.
method Using profinite completions and topology.
result The set of surface words is closed in the profinite topology.
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48 results for “Surface Groups”
Study covers of Chamanara surface with large Veech groups.
problem Characterize finite abelian covers with large Veech groups.
method Analyze Veech groups of finite abelian covers of the Chamanara surface.
result Every free group arises as the projective Veech group of a finite-area infinite translation surface.
Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class groupmath.GT
New groups found that don't virtually algebraically fiber, related to mapping class group orbits.
problem Existence of finite orbits for higher Prym representations of the mapping class group.
method Study of surface-by-surface and surface-by-free groups.
result Existence of free-by-free and free-by-surface groups that do not algebraically fiber.
Division algorithm for surface group rings yields standard complexes and cohomological dimensions.
problem Understanding cohomological dimensions of surface group actions.
method Division algorithm for group rings of surface groups.
result Some 2-complexes with surface fundamental groups are standard.
Characterizes totally elliptic surface group representations into Lie groups.
problem Understanding totally elliptic surface group representations into Lie groups.
method Characterization of representations into and by their mapping properties.
result They are either into a compact subgroup or Deroin--Tholozan representations.
The paper examines subgroup separability for surface and virtual braid groups.
problem Subgroup separability of surface and virtual braid groups.
method Study of subgroup separability (LERF) properties.
result Properties of subgroup separability for surface and virtual braid groups are explored.
Classifies surface Houghton groups and their subgroups up to certain equivalences.
problem Classifying surface Houghton groups and their subgroups.
method Classification based on isomorphism, commensurability, and quasi-isometry.
result Surface Houghton groups and their subgroups classified up to specified equivalences.
Study homology groups of mapping and Torelli groups for surfaces with abelian covers.
problem Understanding the homology of mapping and Torelli groups for surfaces with specific topologies.
method Examined the first homology group of mapping and Torelli groups with coefficients in the first rational homology group of the universal abelian cover of the surface.
result For surfaces with one boundary component, the twisted homology groups are finite-dimensional, but for surfaces with one puncture, they are infinite-dimensional.
Countable modular groups found on surfaces with infinite type.
problem Finding modular groups of infinite type surfaces.
method Proving countable modular groups for orientable infinite type surfaces.
result Every orientable infinite type surface has a countable modular group.
Study of Torelli groups of partitioned surfaces with bounds and asymptotic lengths.
problem Understanding Torelli groups of partitioned surfaces.
method Topological and dynamical analysis of Torelli groups of partitioned surfaces.
result Asymptotic translation lengths of Torelli groups of partitioned surfaces behave almost like the reciprocal of the Euler characteristic of the surface.
The paper provides presentations for mapping class groups and cluster automorphism groups of surfaces.
problem Presentations of mapping class groups of surfaces stabilizing boundaries.
method Gave presentations of mapping class groups of marked surfaces stabilizing boundaries.
result Presented cluster automorphism groups of cluster algebras from surfaces.
Finite groups can be automorphism groups of translation surfaces with poles.
problem Existence of finite automorphism groups on translation surfaces with poles.
method Analyzing translation surfaces with poles and extending results to branched projective structures.
result Finite groups can be automorphism groups of translation surfaces with poles.
Finite presentations for mapping class groups of surfaces and surfaces with points/boundaries.
problem Finding finite presentations for balanced superelliptic mapping class groups.
method Construct finite presentations for corresponding liftable mapping class groups in a different generating set.
result Finite presentations for balanced superelliptic mapping class groups of various surfaces.
Study maps surface configurations to Heisenberg homologies for mapping class groups.
problem Understanding Mapping Class Groups of punctured surfaces.
method Action of mapping classes on Heisenberg homologies of surface configurations.
result Representations of Mapping Class Groups derived from Heisenberg homologies.
Proves incoherence of free-by-free and surface-by-free groups, solving two problems.
problem Proving incoherence of free-by-free and surface-by-free groups.
method Semidirect product construction and virtual algebraic fibering analysis.
result Proves incoherence of free-by-free and surface-by-free groups, answering a question posed by J. Hillman.
We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dens…
Paper studies R∞-property for braid groups on surfaces, proving it for most cases.
problem Investigating the R∞-property for braid groups on orientable surfaces.
method Analyzing surface pure and full braid groups to determine the R∞-property.
result Most surface braid groups have the R∞-property, with exceptions noted.
Study mapping class groups of infinite type surfaces with noncompact boundaries.
problem Classify pure mapping class groups of infinite type surfaces.
method Developed a method to cut surfaces into simpler ones and combined recent results.
result Complete classification of perfect and uniformly perfect pure mapping class groups.
Classifies hyperbolic groups with surface-like boundaries.
problem Classifying hyperbolic groups with specific surface-like boundaries.
method Analyzing quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.
result Identifies hyperbolic groups with surface-like boundaries.
Atoroidal surface bundlesmath.GT
New examples of surface bundles found over surfaces.
problem Finding compact atoroidal surface bundles.
method Type-preserving homomorphism from knot complement to mapping class group.
result Infinitely many commensurability classes of surface subgroups.
Surface Houghton groupsmath.GT
Surface Houghton groups are studied for their mapping class properties.
problem Understanding the mapping class properties of surface Houghton groups.
method Analyzing the asymptotic rigidity and monodromy homeomorphisms of fibered components.
result Surface Houghton groups are of type but not of type .
In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface of genus at least 2, and the number of strings is at least three. This result generalizes previous results for classical …
Study classifies helix surfaces in Lorentzian Heisenberg group.
problem Classifying helix surfaces in Lorentzian Heisenberg group.
method Complete description of ambient space geometry, classification of minimal and CMC helix surfaces, investigation of constant angle surfaces.
result Explicit parametrizations of minimal and CMC helix surfaces in $\htt$.
The study of which mapping class group elements can be realized as affine automorphisms of dilation surfaces.
problem Which elements of the mapping class group can be realized as affine automorphisms of dilation surfaces?
method Investigation into the affine automorphism groups of dilation surfaces, including the construction of dilation surfaces from multicurves.
result Only certain types of mapping class group elements can arise as affine automorphisms of dilation surfaces.
Study shows shorter words for group elements in surface groups and RAAGs.
problem Understanding the structure of surface groups and RAAGs through word lengths.
method Proved lower bounds on shortest words representing nontrivial elements in their lower central series.
result Found that the shortest words are shorter for surface groups and RAAGs.
A translation surface in the Heisenberg group is a surface constructed by multiplying (using the group operation) two curves. We completely classify minimal translation surfaces in the Heisenberg group .
Algorithm constructs surfaces with specific Veech groups in lattice strata.
problem Finding all translation surfaces with a given lattice Veech group.
method Developed an algorithm and provided a new proof of finiteness.
result Algorithm constructs all translation surfaces with a given lattice Veech group.
Classification of groups as symmetries of infinite translation surfaces.
problem Classifying groups as isometry groups of translation surfaces.
method Adapting ideas from hyperbolic surfaces to translation surfaces.
result Every countable subgroup of GL+(2,ℝ) can be realized as the Veech group of a translation surface.
Study homology groups for non-orientable surfaces with boundary.
problem Determine the first homology group for mapping class groups of non-orientable surfaces.
method Calculate the first homology group with twisted coefficients.
result Explicitly determined the first homology group for various mapping class groups.
Geodesic surfaces embed into hyperbolic 3-manifolds for all finite group actions.
problem Embedding geodesic surfaces into hyperbolic 3-manifolds.
method Analyzing finite group actions on surfaces and proving geodesic embeddings for all irreducible cases.
result All quasiplatonic surfaces embed geodesically into hyperbolic 3-manifolds.
We determine which amalgamated products of surface groups identified over multiples of simple closed curves are not fundamental groups of 3-manifolds. We prove each surface amalgam considered is virtually the fundamental group of a 3-manifold. We prove that each such surface group amalgam is abstractly commensurable to…
Proves homology of mapping class groups for infinite-type surfaces.
problem Homology of mapping class groups for infinite-type surfaces.
method Modification of Mather's argument and homological stability result.
result Homology of mapping class groups determined for binary tree surfaces.
Translation surfaces in Heisenberg group classified by Gauss map determinant.
problem Classifying translation surfaces with zero intrinsic curvature in Heisenberg group.
method Constructed surfaces as product of planar curves, classified by Gauss map determinant.
result Surfaces with vanishing intrinsic curvature identified.
The study restricts normal subgroups of Kähler groups, proving specific cases and general restrictions.
problem Characterizing normal subgroups of Kähler groups.
method Analyzing embeddings and conjugation actions of surface groups and one-ended hyperbolic groups.
result Restrictions on normal subgroups of Kähler groups, including virtual direct products and surface group properties.
Study shows pants graph automorphisms match mapping class groups of nonorientable surfaces.
problem Understanding automorphisms of pants graphs on nonorientable surfaces.
method Analyzing mapping class groups and proving isomorphism.
result Automorphism group of pants graphs isomorphic to mapping class groups.
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.
The paper studies Coxeter quotients of surface braid groups.
problem Analyzing Coxeter quotients of surface braid groups.
method Analyzing Coxeter-type quotients of surface braid groups by normal closure and commutator relations.
result Characterized Coxeter quotients of surface braid groups.
Paper uses index theorem to relate symplectic bundle signature to surface group representation in real symplectic group.
problem Relating symplectic bundle signature to surface group representations in real symplectic group.
method Using Atiyah-Patodi-Singer index theorem.
result Obtained a formula for the signature of a flat symplectic vector bundle over a surface with boundary.
Non-proper surface group action on product of trees found.
problem Proper surface group action on product of trees proposed, but not proper.
method Demonstrated non-properness of the surface group action.
result Surface group action on product of trees is not proper.
Groups satisfy linear surface isoperimetric functions.
problem Isoperimetric functions for surface diagrams in hyperbolic groups.
method Analyzing word-hyperbolic groups and their surface diagrams.
result Linear isoperimetric functions for all surface types in hyperbolic groups.
Study automorphism groups of Inoue surfaces using quadratic number fields.
problem Understanding automorphism groups of Inoue surfaces.
method Construction and description of automorphism groups using quadratic number fields.
result Automorphism groups of Inoue surfaces described in terms of quadratic number fields.
Sharp bounds found on nonabelian quotients of surface braid groups.
problem Finding the smallest nonabelian quotients of surface braid groups.
method Sharp lower bounds and classification of quotients.
result Quotients of minimum order are either symmetric groups or 2-step nilpotent p-groups.
Automorphism group of nonorientable surface curve graph matches surface homeomorphisms.
problem Identifying automorphisms of nonorientable surface curve graphs.
method Using Bowden, Hensel, and Webb's fine curve graph and Long, Margalit, Pham, Verberne, and Yao's proof as a foundation.
result Automorphism group of nonorientable surface curve graph is isomorphic to the surface's homeomorphism group.
Surface framed braidsmath.GT
In this paper we introduce the framed pure braid group on strands of an oriented surface, a topological generalisation of the pure braid group . We give different equivalents definitions for framed pure braid groups and we study exact sequences relating these groups with other generalisations of , usually…
Unique minimal translation surfaces found in Heisenberg group.
problem Classifying minimal translation surfaces in Heisenberg group.
method Complete classification through generating curves analysis.
result Uniqueness of minimal translation surfaces up to isometries.
In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was previously announced by Benson Farb for genus at least 4 and has recently been announc…
Smooth surfaces in simply connected 4-manifolds yield groups with non-trivial homology.
problem Finding groups with non-trivial fundamental groups in the complements of surfaces in 4-manifolds.
method Combining topological constructions with homological properties of simple groups.
result The complement of a surface in a simply connected 4-manifold can have a non-trivial fundamental group.
In this paper we generalize the notion of strongly poly-free group to a larger class of groups, we call them strongly poly-surface groups and prove that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for any virtually strongly poly-surface g…