| Résume | Multicomplexes can be viewed as deformations of complexes from an operadic point of view. To each multicomplex, one can associate its total complex, which is a filtered complex and thus gives rise to a spectral sequence. The aim of this presentation is to provide an overview of the results obtained with Sarah Whitehouse (and other collaborators, including J. Cirici, X. Fu, A. Guan, D.E. Santander, and S. Ziegenhagen) concerning homotopy theories of multicomplexes, involving a given page of the associated spectral sequence. We will also present some applications of multicomplexes to complex geometry and to the homology theories of directed graphs, a work in progress with E. Roff. |
