Computing higher leray–serre spectral sequences of towers of fibrations
Computing higher leray–serre spectral sequences of towers of fibrations
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.
1023-1074
Guidolin, Andrea
40011dc4-77ce-4d11-90bd-02e76c0b375a
Romero, Ana
01dcc082-667c-41a7-a7f8-c82e04488cbd
27 October 2020
Guidolin, Andrea
40011dc4-77ce-4d11-90bd-02e76c0b375a
Romero, Ana
01dcc082-667c-41a7-a7f8-c82e04488cbd
Guidolin, Andrea and Romero, Ana
(2020)
Computing higher leray–serre spectral sequences of towers of fibrations.
Foundations of Computational Mathematics, .
(doi:10.1007/s10208-020-09475-8).
Abstract
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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Accepted/In Press date: 5 September 2020
Published date: 27 October 2020
Identifiers
Local EPrints ID: 499971
URI: http://eprints.soton.ac.uk/id/eprint/499971
ISSN: 1615-3375
PURE UUID: ec7bddd0-31e0-494b-852f-05fbe296f75d
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Date deposited: 09 Apr 2025 19:00
Last modified: 10 Apr 2025 02:21
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Author:
Andrea Guidolin
Author:
Ana Romero
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