Gröbner basis on Sullivan minimal models
Hicham YAMOUL · Tue Oct 02, 2012 10:43 pm
We consider a Sullivan minimal model, in the particular case we take an pure Sullivan minimal model, we would like to construct a Gröbner basis in this algebra, note that $d(\Lambda Q\otimes P)=\Lambda Q.d(P)$ is the ideal in the polynomial algebra $\Lambda Q$ generated by $d(P)$. We know that the Gröbner basis is easily computable in many cases, we can determine if two ideals are equal by looking at their reduced Gröbner bases. It is well known that the differential $d$ of any element of $V$ is a polynomial in $\Lambda V$ with no linear term, wich in particular means that there is a homogeneous basis ${v_i}_i\geq 1$ of $V$ for wich $dv_i\in \Lambda V_<i$, where $V_<i$ denotes the subspace of $W$ generated by ${v_i}_j<i, we want to construct by the same manner the Gröbner basis in the Sullivan minimal model as graded algebra, in particular by using the Buchberger’s Criterion, we can then give a set of polynomials with odd degree, by rational dichotomy.