Titlebook: Extended Abstracts GEOMVAP 2019; Geometry, Topology, Maria Alberich-Carramiñana,Guillem Blanco,Eva Mira Conference proceedings 2021 The Ed

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Generating Embeddable Matrices Whose Principal Logarithm is Not a Markov Generator,Several results seem to point out that the embeddability of a Markov process may be determined by checking whether the principal logarithm of its transition matrix is a rate matrix. In this note, we provide a constructive method to produce a positive measure subspace of Markov matrices for which this is not true.

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Dimension Formulas for the Cohomology of Arithmetic Groups,In this extended abstract we will describe a method to study the dimension of the cohomology of an arithmetic group. We will mainly use the Borel-Serre compactification, the theory of cuspidal and Eisenstein cohomology and the Euler characteristic.

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Do Overtwisted Contact Manifolds Admit Infinitely Many Periodic Reeb Orbits?,In this note we discuss an approach to prove existence of infinitely many periodic Reeb orbits in overtwisted contact manifolds. The result is a combination of a plug-like construction and an adaptation of Hofer’s .-holomorphic curve techniques in the case to .-contact manifold.

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Geometry of Non-holonomic Distributions,We consider a non integrable regular distribution . in a Riemannian manifold (., .). Using the Levi-Civita connection in . we extend the geometric notions of fundamental forms, curvature and geodesic curves from submanifolds of (., .) to the distribution . and characterize the totally geodesic distributions in several ways.