C-groups of high rank for the symmetric groups

We give presentations for the C-groups of rank n – 1 of the symmetric group Sn. We also classify C-groups of rank n – 2 for Sn. We show that all these C-groups correspond to regular hypertopes, that is, thin, residually connected flag-transitive geometries. Therefore we generalise some similar results obtained in the framework of string C-groups that are in one-to-one correspondence with abstract regular polytopes.This research was supported by a Marsden grant (UOA1218) of the Royal Society of New Zealand and by the Portuguese funds through the CIDMA – Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), through CIDMA – Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013. The authors also thank an anonymous referee for useful comments on a preliminary version of this paper.publishe

Noncommutative Geometry of Quantized Coverings

This research is devoted to the noncommutative generalization of topological coverings. Otherwise since topological coverings are related to the set of geometric constructions one can obtain noncommutative generalizations of these constructions. Here the generalizations of the universal covering space, fundamental group, homotopy theory, Hurewicz homomorphism, covering of the Riemannian manifold, flat connection are explained. The theory gives pure algebraic proof well known results of the topology and the differential geometry. Besides there are applications of the theory to (unbounded) operator spaces and this theme is also discussed here.Comment: 686 pages, 134 reference

Quanta of Maths

The work of Alain Connes has cut a wide swath across several areas of math- ematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics

Quanta of Maths

The work of Alain Connes has cut a wide swath across several areas of math- ematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics

HERITAGE 2022. International Conference on Vernacular Heritage: Culture, People and Sustainability

Vernacular architecture, tangible and intangible heritage of great importance to European and global culture, represents the response of a society culturally linked to its territory, in terms of climate and landscape. Its construction features are born from the practical experience of the inhabitants, making use of local materials, taking into consideration geographical conditions and cultural, social and constructive traditions, based on the conditions of the surrounding nature and habitat. Above all, it plays an essential role in contemporary society as it is able to teach us important principles and lessons for a respectful sustainable architecture. Vernacular Heritage: Culture, People and Sustainability will be a valuable source of information for academics and professionals in the fields of Environmental Science, Civil Engineering, Construction and Building Engineering and ArchitectureMileto, C.; Vegas López-Manzanares, F.; Cristini, V.; García Soriano, L. (2022). HERITAGE 2022. International Conference on Vernacular Heritage: Culture, People and Sustainability. Editorial Universitat Politècnica de València. https://doi.org/10.4995/HERITAGE2022.2022.15942EDITORIA