Let Hg be a genus g handlebody, and Tg = ∂Hg a closed connected orientable surface. In this paper we find a finite set of generators for Eg 2 , the subgroup of PMCG2(Tg) consisting of the isotopy classes of homeomorphisms of Tg which admit an extension to the handlebody keeping a properly embedded trivial arc fixed. This subgroup turns out to be important for the study of knots in closed 3-mani...

We give a classification of non-orthogonality classes of trivial order 1 strongly minimal sets in differentially closed fields. A central idea is the introduction of τ -forms, functions on the prolongation of a variety which are analogous to 1-forms. Order 1 strongly minimal sets then correspond to smooth projective curves with τ -forms. We also introduce τ -differentials, algebraic versions of...

Let Γ be a lattice in G = SL(n,R) and X = G/S a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish uniform distribution of orbits of Γ in X analogous to the classical equidistribution on torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of Borel subgroup ...

Let H be an abstract group and let C be a variety of finite groups (i.e., a class of finite groups closed under taking subgroups, quotients and finite direct products); for example the variety of all finite p-groups, for a fixed prime p. Consider the smallest topology on H such that all the homomorphism H −→ C from H to any group C ∈ C (endowed with the discrete topology) is continuous. We refe...

Empty p0 p2 . . . pξ pξ+2 . . . Nonempty p1 p3 . . . pξ+1 pξ+3 . . . where pξ, ξ < α, is descending in P and Nonempty wins the game of length α if he can play α times. A poset P is called weakly α-game-closed if Player Nonempty has a winning strategy in the Banach-Mazur game of length α, where Nonempty is allowed to play at limit stages. P is called strongly α-game-closed if Player Nonempty has...

We offer a sufficient condition for a closed subset in an association scheme to be maximal. The result generalizes naturally the well-known (group-theoretical) fact that the one-point-stabilizer of a flag transitive automorphism group of a 2-design with *=1 must be a maximal subgroup. In finite group theory, there exist a lot of (important) sufficient conditions for a subgroup to be maximal. In...

Let X be a normal projective algebraic variety, G its largest connected automorphism group, and A(G) the Albanese variety of G . We determine the isogeny class of A(G) in terms of the geometry of X . In characteristic 0, we show that the dimension of A(G) is the rank of every maximal trivial direct summand of the tangent sheaf of X . Also, we obtain an optimal bound for the dimension of the lar...

The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroup S with a Tychonoff topology T , it is proved that there exists a Hausdorff topological group in which S can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological rig...

The cottontail rabbit herpesvirus is presently classified in subgroup A of the herpesviruses, whereas the virus is strongly cell associated and belongs in subgroup B.

Lattices and parabolic subgroups are the obvious examples of cocompact subgroups of a connected, semisimple Lie group with finite center. We use an argument of C. C. Moore to show that every cocompact subgroup is, roughly speaking, a combination of these. We study a cocompact subgroup H of a connected, semisimple Lie group G with finite center. The case where H is discrete is very important and...