C. A. Abad

activity

20092023

most citedRepresentations up to homotopy of Lie algebroids

21 citations · 64 across the 16 of their papers we have counts for

collaborators

18 papers

gr-qc2023

Relativity

Camilo Arias Abad, Alexander Quintero Velez, Juan Diego Velez Caicedo

These lectures notes contain an introduction to General Relativity. They are addressed to a general mathematical audience with no specific background in physics. The goal is to mot…

math.AT2021★ 1 cited

Chern-Weil theory for $\infty$ -local systems

Camilo Arias Abad, Santiago Pineda Montoya, Alexander Quintero Velez

Let $G$ be a compact connected Lie group. We show that the category $Loc_{\infty} (B G)$ of $\infty$ -local systems on the classifying space of $G$ , can be described infinite…

math.DG2020

The higher Riemann-Hilbert correspondence and principal $2$ -bundles

Camilo Arias Abad, Sebastian Velez Vasquez

In this note we show that the holonomies for higher local systems provided by the higher Riemann-Hilbert correspondence coincide with those associated to principal $2$ -bundles wher…

math.AT2020★ 2 cited

Singular chains on Lie groups and the Cartan relations II

Camilo Arias Abad, Alexander Quintero Velez

Let $G$ be a simply connected Lie group with Lie algebra $g$ and denote by $C_{∙} (G)$ the DG Hopf algebra of smooth singular chains on $G$ . In a companion…

math.AT2019

Singular chains on Lie groups and the Cartan relations I

Camilo Arias Abad

Let $G$ be a simply connected Lie group with Lie algebra $g$ . We show that the following categories are naturally equivalent. The category $Mod (C (G))$ , of suffi…

math.DG2018★ 4 cited

An $A_{\infty}$ version of the Poincaré lemma

Camilo Arias Abad, Alexander Quintero Velez, Sebastian Velez Vasquez

We prove a categorified version of the Poincaré lemma. The natural setting for our result is that of $\infty$ -local systems. More precisely, we show that any smooth homotopy betwee…