Bounded geometry, growth and topology

We characterize functions which are growth types of Riemannian manifolds of bounded geometry.Comment: 15 page

Lagrangian Topology and Enumerative Geometry

We use the "pearl" machinery in our previous work to study certain enumerative invariants associated to monotone Lagrangian submanifolds.Comment: 86 page

Splines in geometry and topology

This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to more thorough treatments of the subject.Comment: 18 page

Supernovae observations and cosmic topology

Two fundamental questions regarding our description of the Universe concern the geometry and topology of its 3-dimensional space. While geometry is a local characteristic that gives the intrinsic curvature, topology is a global feature that characterizes the shape and size of the 3-space. The geometry constrains, but does not dictate the the spatial topology. We show that, besides determining the spatial geometry, the knowledge of the spatial topology allows to place tight constraints on the density parameters associated with dark matter ($\Omega_m$) and dark energy ($\Omega_{\Lambda}$). By using the Poincar\'e dodecahedral space as the observable spatial topology, we reanalyze the current type Ia supenovae (SNe Ia) constraints on the density parametric space $\Omega_{m} - \Omega_{\Lambda}$. From this SNe Ia plus cosmic topology analysis, we found best fit values for the density parameters, which are in agreement with a number of independent cosmological observations.Comment: 5 pages, 2 figures. Minor changes and a ref. added. To appear in A&A (2006