From ca73f708ea12aa6d160e0edd7c86291878598609 Mon Sep 17 00:00:00 2001 From: calquezar Date: Thu, 9 Oct 2025 15:21:10 +0200 Subject: [PATCH] Update README.md --- README.md | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) diff --git a/README.md b/README.md index 341249d..a6c1371 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,21 @@ # AplK +The rational homotopy type of a topological space is a simplified version of the homotopy type, where all homotopy groups are tensored by $\mathbb{Q}$. Despite the lost information, rational homotopy has the advantage of being constructive. Due to Sullivan, for a particular topological space $X$ that satisfies some conditions, it is known theoretically how to obtain its rational homotopy type via the construction of a commutative differential graded algebra, called the Sullivan model of $X$. This algebra is quasi-isomorphic to the normalized singular cochain algebra of $X$, $C^*(X)$, and it allows us to establish a categorical equivalence between homotopy types of spaces and isomorphism classes of Sullivan models: + +$$ +\begin{Bmatrix} +Rational \:\: homotopy +\\ +types \:\: of \:\:spaces +\end{Bmatrix} +\Leftrightarrow +\begin{Bmatrix} +Isomorphim \:\:classes \:\: of +\\ +minimal \:\: Sullivan \:\: models +\end{Bmatrix} +$$ + +In this work it is presented an effective method to compute the Sullivan minimal model for a simply-connected topological space, and an implementation of such method in a Computer Algebra System. In order to illustrate such method, examples of some computations are included. + +This project has been partially supported by PID2020-114750GB-C31 and BES-2017-079979, funded by MCIN/AEI/10.13039/501100011033 and also partially funded by the Departamento de Ciencia, Universidad y Sociedad del Conocimiento of the Gobierno de Aragón (Grupo de referencia E22 20R “Álgebra y Geometría”). \ No newline at end of file