In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects ...

Let $\Phi: \Bbb S^{1}\times M\longrightarrow M$ be a smooth action of the unit circle $\Bbb S^{1}$ on a manifold $M$. In this work, we compute the minimal model of $M$ in terms of the orbit space $B$ and the fixed point ...

We show how to induce products in sheaf cohomology for a wide variety of coefficients: sheaves of dg commutative and Lie algebras, symmetric Omega-spectra, filtered dg algebras, operads and operad algebras.

Let Mg,l be the moduli space of stable algebraic curves of genus g with l marked points. With the operations which relate the different moduli spaces identifying marked points, the family (Mg,l)g,l is a modular operad ...

We prove the existence of Sullivan minimal models of operad algebras, for a quite wide family of operads in the category of complexes of vector spaces over a field of characteristic zero. Our construction is an adaptation ...

Aquest llibre és una introducció a la topologia pensada per a estudiants de la llicenciatura de matemàtiques. Partint dels espais mètrics, s'introdueixen els espais topològics i les aplicacions contínues entre ells, i se ...