arXiv subjects

Antonio Garvin

Publications and source records attributed to Antonio Garvin.

3 recordsLinked to original sources

arXiv2023

Linear models of the exceptional Lie algebra $\mathfrak{e}_8$

This work provides five explicit constructions of the exceptional Lie algebra $\mathfrak{e}_8$, based on its semisimple subalgebras of maximal rank. Each of these models is graded by an abelian group, namely, $\mathbb{Z}_4$, $\mathbb{Z}_5$, $\mathbb{Z}_6$, $\mathbb{Z}_3^2$ and $\mathbb{Z}_2\times\mathbb{Z}_4$; the neutral component is direct sum of special linear algebras and the remaining homogeneous components are irreducible modules for it.

math.RA↗

arXiv2019

An algorithm to compute minimal Sullivan algebras

In this note, we give an algorithm that starting with a Sullivan algebra gives us its minimal model. This algorithm is a kind of modified AT-model algorithm used to compute in the past other kinds of topology information such as (co)homology, cup products on cohomology and persistent homology. Taking as input a (non-minimal) Sullivan algebra $A$ with an ordered finite set of generators preserving the filtration defined on $A$, we obtain as output a minimal Sullivan algebra with the same rational cohomology as $A$.

math.AT↗

arXiv2018

Rational maps from Euclidean Configuration Spaces to Spheres

In this note we give an algorithm to determine the rational homotopy type of the free and pointed mapping spaces $ map(F(\mathbb R^m,k), S^n)$ and $ map^*(F(\mathbb R^m,k), S^n)$. An explicit description of these spaces is given for $k=3$. The general case for $n$ odd is also presented as an immediate consequence of the rational version of a classical result of Thom.

math.AT↗