Galois conjugates of pseudo-Anosov stretch factors are dense in the complex plane.
problem Understanding the distribution of Galois conjugates of pseudo-Anosov stretch factors.
method Using Penner's construction of pseudo-Anosov mapping classes, we show density in the complex plane.
result Galois conjugates of stretch factors arising from Penner's construction are dense in the complex plane.
Characterizes bi-Perron numbers with specific Galois conjugates.
problem Understanding bi-Perron numbers with real or unimodular conjugates.
method Characterization through power properties and spectral radii of transformations.
result Bi-Perron numbers with real or unimodular conjugates admit a power as stretch factors or spectral radii.
The paper disproves a question about complex projective plane curves.
problem Disproving a question about arithmetic Zariski pairs.
method Using complement-equivalent arithmetic Zariski pairs and braid monodromy factorization.
result Answered in the negative a question by Eyral-Oka on these curves and their groups.
New research shows non-isomorphic fundamental groups for a pair of line arrangements.
problem Proving non-isomorphic fundamental groups for line arrangements.
method Analyzing fundamental groups of complements of line arrangements.
result Fundamental groups of complements of line arrangements are not isomorphic.
Study stretch factors on nonorientable surfaces, proving nonorientable techniques ineffective.
problem Determine stretch factors on nonorientable surfaces.
method Analyzing pseudo-Anosov maps with orientable foliations on specific surfaces.
result Stretch factors do not have Galois conjugates on the unit circle.
We show that Galois conjugates of stretch factors of pseudo-Anosov mapping classes arising from Penner's construction lie off the unit circle. As a consequence, we show that for all but a few exceptional surfaces, there are examples of pseudo-Anosov mapping classes so that no power of them arises from Penner's construc…
Constructs pseudo-Anosov homeomorphisms using positive twists.
problem Creating explicit examples of pseudo-Anosov maps with specific properties.
method Using positive half-twists to construct pseudo-Anosov homeomorphisms on n-times punctured spheres and surfaces with higher genus.
result Produces examples of pseudo-Anosov maps with non-trivial trace fields and unit circle Galois conjugates.
We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension 2. We prove a Mertens' formula for the integer points over a quadratic imaginary num…
New Fuchsian groups found with special embedding properties.
problem Finding new Fuchsian groups with specific embedding properties.
method Using period domains and properties of complex hyperbolic surfaces.
result First cocompact nonarithmetic Fuchsian groups with modular embedding not commensurable with triangle groups.
One of the main themes of this long article is the study of projective varieties which are K(H,1)'s, i.e. classifying spaces BH for some discrete group H. After recalling the basic properties of such classifying spaces, an important class of such varieties is introduced, the one of Bagnera-de Franchis varieties, the qu…