On minimal models in integral homotopy theory (Q1605636)

Inspired by some ideas of A. Grothendieck, the author shows that any nilpotent finite homotopy type can be represented by a simplicial set given by a finitely generated free abelian group and its canonical maps are represented by polynomials with rational coefficients. In particular, the space \(K(G,1)\) leads to a close relation with the theory of Passi polynomials [\textit{I. B. S. Passi}, J. Algebra 9, 152--182 (1968; Zbl 0159.31503)], provided \(G\) is a torsion free finitely generated nilpotent group. Passing to the rational localization, the theory is compared with the theories of \textit{D. Quillen} [Ann. Math. (2) 90, 205--295 (1969; Zbl 0191.53702)] and \textit{D. Sullivan} [Publ. Math., Inst. Hautes Études Sci. 47, 269--331 (1977; Zbl 0374.57002)].