arXiv subjects

Federico Cantero-Morán

Publications and source records attributed to Federico Cantero-Morán.

4 recordsLinked to original sources

arXiv2024

On the scanning map and the space of smooth projective hypersurfaces

The space of degree d smooth projective hypersurfaces of CP n admits a scanning map to a certain space of sections. We compute a rational homotopy model of the action by conjugation of the group U (n + 1) on this space of sections, from which we deduce that the scanning map induces a monomorphism on cohomology when d > 2. Our main technique is the rational homotopy theory of Sullivan and, more specifically, a Sullivan model for the action by conjugation of a connected topological group on a space of sections.

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arXiv2024

Connected power operations and simplicial Poincaré duality

We introduce a structure termed ``connected cyclic diagonal'' on a chain complex, which induces stable power operations in its cohomology with the property that negative power operations consistently vanish. This chain level structure is useful to represent power operations for spectra, whose cohomology lacks a cup product. Using a Poincaré duality algebra structure on the integral chains of the standard augmented simplex, we provide an effective method for the construction of cyclic diagonals on a broad class of augmented simplicial objects.

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arXiv2023

Quantum annular homology and bigger Burnside categories

As part of their construction of the Khovanov spectrum, Lawson, Lipshitz and Sarkar assigned to each cube in the Burnside category of finite sets and finite correspondences, a finite cellular spectrum. In this paper we extend this assignment to cubes in Burnside categories of infinite sets. This is later applied to the work of Akhmechet, Krushkal and Willis on the quantum annular Khovanov spectrum with an action of a finite cyclic group: we obtain a quantum annular Khovanov spectrum with an action of the infinite cyclic group.

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arXiv2023

An effective proof of the Cartan formula: Odd primes

The Cartan formula relates the cup product and the action of the Steenrod algebra on mod~$p$ cohomology. For any pair of mod $p$ cocycles in a simplicial set, where $p$ is an odd prime, we effectively construct a natural coboundary descending to this formula in cohomology.

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