Affine configurations and pure braids

We show that the fundamental group of the space of ordered affine-equivalent configurations of at least five points in the real plane is isomorphic to the pure braid group modulo its centre. In the case of four points this fundamental group is free with eleven generators.Comment: 5 pages, 1 figure, final version; to appear in Discrete & Computational Geometry, available from the publishers at http://www.springerlink.com/content/384516n7q24811ph

Análisis de las actuaciones de protección ambiental y gestión turística en el Parque Regional de Calblanque, Monte de las Cenizas y Peña del Águila (Murcia, SE España)

The Regional Park of Calblanque, Monte de las Cenizas and Peña del Águila has 2,822 hectares and more than 13 km of coastline in the municipalities of Cartagena and La Union. With the objective of evaluating the management, environmental and tourist conservation between 2000-2017, the analysis of the reports and reports of the administration is used as a methodology. The result is the participation of 7 professionals, an annual budget of over 600 thousand euros for maintenance and cleaning, surveillance, information and visitor assistance, infrastructures and equipment for public use, conservation of some salt mines, the Tetraclinis articulata forest and limitation of vehicle accesses in summer.El Parque Regional de Calblanque, Monte de las Cenizas y Peña del Águila tiene 2.822 ha y más de 13 Km de costa en los municipios de Cartagena y la Unión. Con el objetivo de evaluar la gestión, conservación ambiental y turística entre 2000-2017, se utiliza como metodología el análisis de las memorias e informes de la administración. El resultado es la participación de 7 profesionales, un presupuesto anual superior a 600 mil euros para mantenimiento y limpieza, vigilancia, información y atención al visitante, infraestructuras y equipamientos de uso público, conservación de unas salinas, del bosque de Tetraclinis articulata y limitación de accesos de vehículos en verano

The volume flux group and nonpositive curvature

We show that every closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume, and admits a finite covering with circle actions whose orbits are homologically essential. This proves a conjecture of Kedra-Kotschick-Morita for this class of manifolds.Comment: 6 pages, final version, to appear in Ann. Global Analysis and Geometr

Theoretical study of topological properties of ferromagnetic pyrite CoS₂

Since the discovery of the first topological material 15 years ago, the search for material realizations of novel topological phases has become the driving force of the field. While oftentimes we search for new materials, we forget that well established materials can also display very interesting topological properties. In this work, we revisit CoS2, a metallic ferromagnetic pyrite that has been extensively studied in the literature due to its magnetic properties. We study the topological features of its electronic band structure and identify Weyl nodes and nodal lines, as well as a symmetry-protected fourfold fermion close to the Fermi level. Looking at different surface cleavage planes, we observe both spin polarized Fermi arcs in the majority channel and drumhead states. These findings suggest that CoS2 is a promising platform to study topological phenomena, as well as a good candidate for spintronic applications