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Online Seminar: Homotopy theories of multi complexes April 21, 2020 (10:00 AM PDT - 11:30 AM PDT)
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Location: MSRI: Online/Virtual
Speaker(s) Muriel Livernet (Institut de Mathematiques de Jussieu)
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Homotopy Theories Of Multi Complexes


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Multicomplexes (also known as twisted complexes) are a generalization of  bicomplexes introduced by Wall in the sixties, and frequently encountered in different contexts. They yield to filtered complexes, then to spectral sequences, and thus to a family of weak equivalences, called E_r-equivalences: a morphism f of multicomplexes is an E_r-equivalence if it is an isomorphism at the r+1-stage of the associated spectral sequence. In joint works with Sarah Whitehouse, Joana Cirici, Daniela Egas Santander and with Xin Fu and Ai Gan, we proved that there is a cofibrantly generated model category structure on multicomplexes with weak equivalences being E_r-equivalences. The purpose of the talk is to motivate this work, give some details on the constructions and proof, and present some work in progress.

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Homotopy Theories Of Multi Complexes

H.264 Video 24980_28332_8285_Homotopy_Theories_of_Multi_Complexes.mp4