31 research outputs found
Uniform hyperbolicity of the curve graph via surgery sequences
We prove that the curve graph \calC^{(1)}(S) is Gromov-hyperbolic with a
constant of hyperbolicity independent of the surface . The proof is based on
the proof of hyperbolicity of the free splitting complex by Handel and Mosher,
as interpreted by Hilion and Horbez.Comment: 18 pages, 3 figure
Equivariant dendroidal sets and simplicial operads
We establish a Quillen equivalence between the homotopy theories of
equivariant Segal operads and equivariant simplicial operads with norm maps.
Together with previous work, we further conclude that the homotopy coherent
nerve is a right-Quillen equivalence from the model category of equivariant
simplicial operads with norm maps to the model category structure for
equivariant--operads in equivariant dendroidal sets.Comment: v3: Improvements to exposition and minor edits, in response to
referee suggestion
Saturated fusion systems with parabolic families
Let G be group; a finite p-subgroup S of G is a Sylow p-subgroup if every
finite p-subgroup of G is conjugate to a subgroup of S. In this paper, we
examine the relations between the fusion system over S which is given by
conjugation in G and a certain chamber system C, on which G acts chamber
transitively with chamber stabilizer N_G(S). Next, we introduce the notion of a
fusion system with a parabolic family and we show that a chamber system can be
associated to such a fusion system. We determine some conditions the chamber
system has to fulfill in order to assure the saturation of the underlying
fusion system. We give an application to fusion systems with parabolic families
of classical type.Comment: 28 page
Khinchin theorem for interval exchange transformations
We define a diophantine condition for interval exchange transformations
(i.e.t.s). When the number of intervals is two, that is for rotations on the
circle, our condition coincides with classical Khinchin condition. We prove for
i.e.t.s the same dichotomy as in Khinchin Theorem. We also develop several
results relating the Rauzy-Veech algorithm with homogeneous approximations for
i.e.t.s.Comment: 53 page