Fixed point free action with regular orbits.
Making use of the Nielsen fixed point theory, we study a conjugacy invariant of braids, which we call the level index function. We present a simple algorithm for computing it for positive permutation cyclic braids.
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
We generalize Colliot-Thélène’s construction of flasque resolutions of reductive group schemes over a field to a broad class of base schemes.
In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales.We show that some such results remain valid for metric spaces with non-unique geodesic segments under suitable convexity assumptions on the distance function along distinguished geodesics. The discussion includes, among other things, the Flat Torus Theorem and Gromov’s hyperbolicity criterion referring to embedded planes. This generalizes...
The isoperimetric inequality |∂Ω| / |Ω| = constant / log |Ω| for finite subsets Ω in a finitely generated group Γ with exponential growth is optimal if Γ is polycyclic.
An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.
Nous démontrons que dans la catégorie des foncteurs entre espaces vectoriels sur , le produit tensoriel entre le second foncteur injectif standard non constant et un foncteur puissance extérieure est artinien. Seul était antérieurement connu le caractère artinien de cet injectif ; notre résultat constitue une étape pour l’étude du troisième foncteur injectif standard non constant de .Nous utilisons le foncteur de division par le foncteur identité et des considérations issues de la théorie...