5 papers
Polar Coordinates and Fundamental Group
Jules Chenal
In this article, we investigate the relationship between the fundamental group of a space and its continuous transformations. To be more precise, we show that if a continuous actio…
Real Toric Varieties: Interactions between their Geometry and their Topology
Jules Chenal, Matilde Manzaroli
In the present article, we investigate the topology of real toric varieties, especially those whose torus is not split over the field of real numbers. We describe some canonical fi…
On the First Page of the Renaudineau-Shaw Spectral Sequence
Jules Chenal
In this article, we study the topology of T-hypersurfaces. These cellular hypersurfaces are generalisations of the cellular complexes used to describe the real loci of varieties ob…
Poincaré Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces
Jules Chenal
In this article, we present two structural results about the Renaudineau-Shaw spectral sequence that computes the cohomology of T-hypersurfaces. The first is a Poincaré duality sat…
A Poincaré-Lefschetz Theorem for Cellular Cosheaves and an Application to the Tropical Homology of Orbifold Toric Varieties
Jules Chenal
We begin by presenting a version of the Poincaré-Lefschetz theorem for certain cellular cosheaves on a particular subdivision of a CW-complex K. To that end we construct a cellular…