A generalization of effective Serre spectral systems for m-multicomplexes

• Miguel, Daniel ^[1] ; Andrea Guidolin ^[1] ; Ana Romero ^[1] ; Julio Rubio ^[1]
  1. [1] Universidad de La Rioja

     Universidad de La Rioja

     Logroño, España

     
• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 123-126
• Idioma: inglés
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• Resumen

  • In a previous study, we gave an algorithm to construct a spectral system from a tower of fibrations of simplicial sets, which encompasses all the information provided by the successive Serre spectral sequences of each fibration. The spectral system was builtover generalized multicomplexes that come from the associated chain complexes of the simplicial sets. In this work we show that a similar spectral system can be constructed over a broader class of multicomplexes, and that we have effective homology for it.