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Reduced Bers boundaries of Teichmüller spaces

Ken’ichi Ohshika (2014)

Annales de l’institut Fourier

We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space lying there into a point.This boundary turns out to be independent of the basepoint, and the action of the mapping class group extends continuously to this boundary.This is an affirmative answer to Thurston’s conjecture.He also conjectured that this boundary is homeomorphic to the unmeasured lamination space by the correspondence coming...

Reeb vector fields and open book decompositions

Vincent Colin, Ko Honda (2013)

Journal of the European Mathematical Society

We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux.We study two cases: when the monodromy map of the compatible open book is periodic and when it is pseudo-Anosov. For an open book with periodic monodromy, we verify the Weinstein conjecture. In the case of an open book with pseudo-Anosov monodromy, suppose the boundary of a page of the open book is connected and the fractional Dehn twist coefficient c equals k = n , where...

Regenerating hyperbolic cone 3-manifolds from dimension 2

Joan Porti (2013)

Annales de l’institut Fourier

We prove that a closed 3-orbifold that fibers over a hyperbolic polygonal 2-orbifold admits a family of hyperbolic cone structures that are viewed as regenerations of the polygon, provided that the perimeter is minimal.

Regular projectively Anosov flows on three-dimensional manifolds

Masayuki Asaoka (2010)

Annales de l’institut Fourier

We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of T 2 × I -models. We also apply our method to rigidity problems of some group actions.

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