Universidade do Minho, Braga, Portugal
27 de novembro de 2013

Resumos

José Manuel García Calcines (Univ. La Laguna, Espanha)
Brown representability for exterior cohomology and cohomology with compact supports

It is well known that cohomology with compact supports is not a homotopy invariant but only a proper homotopy one. However, as the proper category lacks of general categorical properties, a Brown representability theorem type does not seem reachable. However, by proving such a theorem for the so called exterior cohomology in the complete and cocomplete exterior category, we show that the nth. cohomology with compact supports of a given locally finite relative CW-complex (X,IR+) is naturally identified with the set [Kn, X]IR+ of exterior, based, homotopy clases from a certain "classifying space" Kn.

João Miguel Nogueira (Univ. de Coimbra, Portugal)
Tunnel number degeneration under the connected sum of prime knots

In this talk we present a study on 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by more than one: t(K1 # K2 )≥ t(K1)+t(K2)-1, for K1 and K2 prime knots.

Ana Pereira do Vale (Univ. do Minho, Portugal)
Chord Geometry

The two dimensional and the three dimensional chord models developed by Dimitri Tymoczko. We will see some geometric properties of this model and their musical meaning.

Antonio De Nicola (Univ. de Coimbra, Portugal)
Hard Lefschetz Theorem for Sasakian manifolds

It is well known that in any compact Kähler manifold the exterior multiplication by suitable powers of the symplectic form induces isomorphisms between the de Rham cohomology spaces of complementary degrees. This is the content of the celebrated Hard Lefschetz Theorem. In my talk I will present recent joint work with B. Cappelletti Montano and I. Yudin showing the existence of similar isomorphisms for compact Sasakian manifolds. We prove that such isomorphisms are independent of the choice of any compatible Sasakian metric on a given contact manifold. As a consequence, we find an obstruction for a contact manifold to admit compatible Sasakian structures.

Thomas Kahl (Univ. do Minho, Portugal)

Topological abstraction of higher dimensional automata

Higher dimensional automata constitute one of the most expressive models for concurrent systems. By definition, an HDA is a precubical set (i.e. a cubical set without degeneracies) with labels on edges. An important practical problem in concurrency theory is the fact that models of systems can easily become very large. This is called the state space explosion problem. In this talk, I will discuss topological abstraction of higher dimensional automata, i.e the replacement of an HDA by a smaller one that is topologically equivalent and models the same system.

Ana Cristina Ferreira (Univ. do Minho, Portugal)

On the classification of naturally reductive homogeneous spaces in small dimensions

A homogeneous space is naturally reductive if it carries a metric connection with skew torsion that has parallel torsion and parallel curvature - they are hence a natural generalisation of symmetric spaces. Based on recent progress on holonomy of metric connections with skew torsion, we sketch our work on the classication of naturally reductive homogeneous spaces of dimension less or equal to 6 by endowing them with an induced geometric structure. We explain how this approach differs from the classical techniques of Kowalski and Vanhecke, who made this classication up to dimension 5 in the mid 80ies.