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A new proof of the virtual Haken conjecture
Charalampos Charitos
A new direct proof of the Virtual Haken Conjecture, which asserts that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group has a finit…
Essential closed surfaces and finite coverings of negatively curved cusped 3-manifolds
Charalampos Charitos
The existence of essential closed surfaces surfaces is proven for finite coverings of 3-manifolds that are triangulated by finitely many topological ideal tetrahedra and admit a re…
Morse foliations of codimension one on the sphere S^3
Charalampos Charitos
Morse foliations of codimension one on the sphere S^3 are studied and the existence of special components for these foliations is derived. As a corollary the instability of Morse f…
On the Complex of Separating meridians in Handlebodies
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
For a handlebody of genus it is shown that every automorphism of the complex of separating meridians can be extended to an automorphism on the complex of all meridians and…
On the geodesic flow on CAT(0) spaces
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
Under certain assumptions on CAT(0) spaces, we show that the geodesic flow is topologically mixing. In particular, the Bowen-Margulis' measure finiteness assumption used in recent…
On surfaces with conical singularities of arbitrary angle
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesic…
The geometry of Euclidean surfaces with conical singularities
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed…
On the homeomorphisms of the space of geodesic laminations on a hyperbolic surface
Charalampos Charitos, Ioannis Papadoperakis, Athanase Papadopoulos
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 th…
A Complex of Incompressible Surfaces for handlebodies and the Mapping Class Group
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
For a genus g handlebody H a simplicial complex, with vertices being isotopy classes of certain incompressible surfaces in H, is constructed and several properties are established.…
Generalized Teichmüller space of non-compact 3-manifolds and Mostow rigidity
Charalampos Charitos, Ioannis Papadoperakis
Consider a 3dimensional manifold obtained by gluing a finite number of ideal hyperbolic tetrahedra via isometries along their faces. By varying the isometry type of each tet…
Essential disks and semi-essential surfaces in 3-manifolds
Charalampos Charitos, Ulrich Oertel
If M is a manifold with compressible boundary, we analyze essential disks in M, as well as incompressible, but not necessarily boundary incompressible, surfaces in M. We are most i…
On the Mapping class group of a genus 2 handlebody
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
A complex of incompressible surfaces in a handlebody is constructed so that it contains, as a subcomplex, the complex of curves of the boundary of the handlebody. For genus 2 handl…