arXiv research

Study weak conjugacy in surface homeomorphisms.

Goldman bracket distinguishes surface homeomorphisms.

Study shows certain surface homeomorphisms groups can't be precompact.

Generates special homeomorphisms for complex surfaces.

The study of periodic subgroups in homeomorphism groups of manifolds.

Automorphism group of nonorientable surface curve graph matches surface homeomorphisms.

Classifies semi-algebraic surfaces up to bi-Lipschitz homeomorphisms.

Automorphisms of fine curve graphs match surface homeomorphisms for planar surfaces.

Minimal topology on surface homeomorphisms proven.

New proof associates partitions to isotopic pseudo-Anosov homeomorphisms.

Study covers of surfaces, showing types and properties.

We prove that for any orientable connected surface of finite type which is not a a sphere with at most four punctures or a torus with at most two punctures, any homeomorphism of the space of geodesic laminations of this surface, equipped with the Thurston topology, is induced by a homeomorphism of the surface.

Characterizes quasiconformal homeomorphisms on surfaces.

Finite groups act freely on surfaces but not on 3-manifolds.

New projection complex shows some surface homeomorphisms have positive commutator length.

Paper confirms conjecture for PL foliations of codimension 2.

Study shows certain mapping class groups cannot be realized as subgroup of homeomorphisms.

Automorphisms of fine 1-curve graph linked to surface homeomorphisms.

Automorphisms of fine curve graph match surface homeomorphisms.

Classifies when homeomorphism groups of stable surfaces have automatic continuity.

Countable modular groups found on surfaces with infinite type.

Study finds infinitely many surface bundle types with zero signature.

The Epstein-Baer theory of curve isotopies is basic to the remarkable theorem that homotopic homeomorphisms of surfaces are isotopic. The groundbreaking work of R. Baer was carried out on closed, orientable surfaces and extended by D. B. A. Epstein to arbitrary surfaces, compact or not, with or without boundary and ori…

We prove that for any non-compact connected surface $M$ the group $H_c(M)$ of compactly suported homeomorphisms of $M$ endowed with the Whitney topology is homeomorphic to $R^\infty\times l_2$ or $Z\times R^\infty\times l_2$.

Study shows infinite-dimensional third bounded cohomology for non-orientable surfaces.

Study surfaces in 4-manifolds with cyclic fundamental group.

Every weak Perron number is realized as a stretch factor of a homeomorphism on a surface.

Minimal stretch factor for non-orientable surfaces is small.

Bestvina and Handel have found an effective algorithm that determines whether a given homeomorphism of an orientable, possibly punctured surface is pseudo-Anosov. We present a software package in Java that realizes this algorithm for surfaces with one puncture. Moreover, the package allows the user to define homeomorph…

Study arcs on surfaces, focusing on topological aspects and group actions.

Upper bound on 3-manifold volumes from surface homeomorphisms.

The closure of a braid in a closed orientable surface $Σ$ is a link in $Σ\times S^1$. We classify such closed surface braids up to isotopy and homeomorphism (with a small indeterminacy for isotopy of closed sphere braids), algebraically in terms of the surface braid group. We find that in positive genus, braids close t…

Study on homeomorphisms preserving $C^1$ curves on surfaces.

Study automorphisms of smooth curve graphs on surfaces.

We prove two rigidity results for automorphism groups of the spaces ML(S) of measured laminations on a closed hyperbolic surface S and PML(S) of projective measured laminations on this surface. The results concern the homeomorphisms of ML(S) that preserve the geometric intersection between laminations and the homeomorp…

Flat fully augmented links with homeomorphic complements are equivalent.

We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham's proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surf…

We prove the existence of homeomorphisms of a closed, orientable surface of genus 3 or greater that do not extend to any handlebody bounded by the surface. We show that such homeomorphisms exist arbitrarily deep in the Johnson filtration of the mapping class group. The second and third terms of the Johnson filtration a…

Automorphisms of fine graphs for surfaces and tori are studied.

Paper finds optimal pseudo-Anosov homeomorphisms for surfaces with specific properties.

Study homeomorphisms on fine curve graph of surfaces, revealing new types of dynamics.

Finite-type surfaces have a topological Hopf property.

Study of homeomorphisms on infinite type surfaces with a classification theorem.

We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.

The study connects periodic surface homeomorphisms to contact structures using rational open books.

Algorithm classifies surface homeomorphisms with polynomial time complexity.

We generalize a classical result concerning smooth germs of surfaces, by proving that monodromies on links of isolated complex surface singularities associated with reduced holomorphic map germs admit a positive factorization. As a consequence of this and a topological characterization of these monodromies by Anne Pich…

This thesis classifies pseudo-Anosov homeomorphisms using geometric Markov partitions.