Denote by , , the regular tree whose vertices have valence , its boundary. Yu. A. Neretin has proposed a group of transformations of , thought of as a combinatorial analogue of the diffeomorphism group of the circle. We show that is generated by two groups: the group of tree automorphisms, and a Higman-Thompson group . We prove the simplicity of and of a family of its subgroups.
We define the singular Hecke algebra as the quotient of the singular braid monoid algebra by the Hecke relations , . We define the notion of Markov trace in this context, fixing the number of singular points, and we prove that a Markov trace determines an invariant on the links with singular points which satisfies some skein relation. Let denote the set of Markov traces with singular points. This is a -vector space. Our main result is that is of dimension . This result is completed...
Let X be a one-dimensional Peano continuum. Then the singular homology group H₁(X) is isomorphic to a free abelian group of finite rank or the singular homology group of the Hawaiian earring.
On montre que les composantes irréductibles du lieu singulier d’une variété de Schubert dans associée à une permutation covexillaire, sont paramétrées par certains des points coessentiels du graphe de la permutation. On donne une description explicite de ces composantes et l’on décrit la singularité le long de chacune d’entre elles.
We define for each group G the skein algebra of G. We show how it is related to the Kauffman bracket skein modules. We prove that skein algebras of abelian groups are isomorphic to symmetric subalgebras of corresponding group rings. Moreover, we show that, for any abelian group G, homomorphisms from the skein algebra of G to C correspond exactly to traces of SL(2,C)-representations of G. We also solve, for abelian groups, the conjecture of Bullock on SL(2,C) character varieties of groups - we show...
Under a multigraph it is meant in this paper a general incidence structure with finitely many points and blocks such that there are at least two blocks through any point and also at least two points on any block. Using submultigraphs with saturated points there are defined generating point sets, point bases and point skeletons. The main result is that the complement to any basis (skeleton) is a skeleton (basis).