The following problem is considered: when can the action of a cancellative semigroup S on a set be extended to a simply transitive action of the universal group of S on a larger set.

A small part of real line which is very close to zero has rich combinatorial properties. The aim this paper express and then prove some locally concepts near a virtual idempotent by considering the wap -compactification semitopological semigroup id="M2"> S . id="M3"> id="M4"> , denoted id="M5"> <mro...

The Higson compactification of any simply connected proper geodesic metric space admits an embedding into a product adelic solenoids that induces isomorphism 1-dimensional cohomology. the universal covering Y‾ finite complex Y supplied with lifted from π1(Y)-equivariant epimorphism

We compute all the top intersection numbers of divisors on the total space of the Poincaré bundle restricted to B × C (where B is an abelian variety, and C ⊂ B is any test curve). We use these computations to find the class of the universal theta divisor and mtheta divisor inside the universal corank 1 semiabelian variety — the boundary of the partial toroidal compactification of the moduli spa...

We determine explicitly the Picard groups of the universal Jacobian stack and of its compactification over the stack of stable curves. Along the way, we prove some results concerning the gerbe structure of the universal Jacobian stack over its rigidification by the natural action of the multiplicative group and relate this with the existence of generalized Poincaré line bundles. We also compare...

We compute all the top intersection numbers of divisors on the total space of the Poincaré bundle restricted to B × C (where B is an abelian variety, and C ⊂ B is any test curve). We use these computations to find the class of the universal theta divisor and mtheta divisor inside the universal corank 1 semiabelian variety — the boundary of the partial toroidal compactification of the moduli spa...

We show that for a discrete semigroup S there exists a uniquely determined complete Boolean algebra B(S) the algebra of clopen subsets of M(S). M(S) is the phase space of the universal minimal dynamical system for S and it is an extremally disconnected compact Hausdorff space. We deal with this connection of semigroups and complete Boolean algebras focusing on structural properties of these alg...

We introduce strong Morita equivalence for inverse semigroups. This notion encompasses Mark Lawson’s concept of enlargement. Strongly Morita equivalent inverse semigroups have Morita equivalent universal groupoids in the sense of Paterson and hence strongly Morita equivalent universal and reduced C∗-algebras. As a consequence we obtain a new proof of a result of Khoshkam and Skandalis showing t...

0.1. Motivation and Goal. The problem of finding a natural relative compactification of the relative Jacobian over a family of curves has drawn a lot of attention since Igusa’s pioneering work [18] in the fifties. (In Subsect. 0.2 the reader will find a slightly more detailed account of this history, with references.) In the case where the curves in the family are geometrically integral, a very...