Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations

Guidolin Andrea; Romero Ana

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Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations

机译：Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations

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摘要

The higher Leray–Serre spectral sequence associated with a tower of fibrations represents a generalization of the classical Leray–Serre spectral sequence of a fibration. In this work, we present algorithms to compute higher Leray–Serre spectral sequences leveraging the effective homology technique, which allows to perform computations involving chain complexes of infinite type associated with interesting objects in algebraic topology. In order to develop the programs, implemented as a new module for the Computer Algebra system Kenzo, we translated the original construction of the higher Leray–Serre spectral sequence in a simplicial framework and studied some of its fundamental properties.

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《Foundations of computational mathematics》 |2021年第4期|1023-1074|共52页
作者
Guidolin Andrea; Romero Ana;
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作者单位

Basque Center for Applied Mathematics;

University of La Rioja;

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原文格式 PDF
正文语种英语
中图分类应用数学;
关键词
Symbolic computation; Constructive Algebraic Topology; Computational topology; Higher spectral sequences; Leray–Serre spectral sequence; Effective homology.; 68W30; 55T05; 55T10; 18N50.;

Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations

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