A free group acting without fixed points on the rational unit sphere
A free group of piecewise linear transformations
We prove the following conjecture of J. Mycielski: There exists a free nonabelian group of piecewise linear, orientation and area preserving transformations which acts on the punctured disk {(x,y) ∈ ℝ²: 0 < x² + y² < 1} without fixed points.
A Free Product with a Non-Power Amalgamated which is not Residually Free.
A Frobenius formula for the characters of the Hecke algebras.
A Frobenius Theorem for Blocks.
A functional treatment of right invariant holoids.
A Functorial Transfer Theorem.
A Galois -groupoid for -difference equations
We first recall Malgrange’s definition of -groupoid and we define a Galois -groupoid for -difference equations. Then, we compute explicitly the Galois -groupoid of a constant linear -difference system, and show that it corresponds to the -difference Galois group. Finally, we establish a conjugation between the Galois -groupoids of two equivalent constant linear -difference systems, and define a local Galois -groupoid for Fuchsian linear -difference systems by giving its realizations.
A Game Theoretical Approach to The Algebraic Counterpart of The Wagner Hierarchy : Part II
The algebraic counterpart of the Wagner hierarchy consists of a well-founded and decidable classification of finite pointed ω-semigroups of width 2 and height ωω. This paper completes the description of this algebraic hierarchy. We first give a purely algebraic decidability procedure of this partial ordering by introducing a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of any ω-rational language can therefore be computed...
A game theoretical approach to the algebraic counterpart of the Wagner hierarchy : Part I
The algebraic study of formal languages shows that ω-rational sets correspond precisely to the ω-languages recognizable by finite ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on...
A GAP package for braid orbit computation and applications.
A Garside presentation for Artin-Tits groups of type
We prove that an Artin-Tits group of type is the group of fractions of a Garside monoid, analogous to the known dual monoids associated with Artin-Tits groups of spherical type and obtained by the “generated group” method. This answers, in this particular case, a general question on Artin-Tits groups, gives a new presentation of an Artin-Tits group of type , and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof...
A Gauss-Bonnet formula for discrete arithmetically defined groups
A Gel'fand model for a Weyl group of type .
A general coordinatization principle for projective planes with comparison of Hall and Hughes frames and with examples of generalized oval frames
A general finite basis condition for systems of semigroup identities.
A general theory of structure spaces
A generalization of a theorem of A. D. Otto.
A generalization of a theorem of F. Richman and C. P. Walker
A generalization of a theorem of Minkowski