Research

Lines and works

PhD thesis

Title of the thesis: Effective homology and spectral sequences
Supervisors: Julio Rubio García (UR) and Francis Sergeraert (Institut Fourier, Grenoble)
Complete pdf file.

Spectral sequences

• Spectral sequences associated with filtered complexes:
  Computing Spectral Sequences. A paper published in Journal of Symbolic Computation 41, pp 1059-1079 (2006). Joint work with J. Rubio and F. Sergeraert.
  Lisp files implementing our algorithms.
• Bousfield-Kan spectral sequence:
  An algorithm computing the first two levels of the Bousfield-Kan spectral sequence. A paper puplished in Appl. Algebra Eng. Commun. Comput. 21(3), pp. 227-248 (2010).
  Some Lisp files.

Effective homology and homology of groups

• Interoperating between Computer Algebra systems: computing homology of groups with Kenzo and GAP. A paper published in International Symposium on Symbolic and Algebraic Computation, ISSAC 2009, pp. 303-310 (2009). Joint work with G. Ellis (National University of Ireland, Galway) and J. Rubio.
• Lisp files
  
• Translator GAP -> OpenMath
• OpenMath content dictionary
  
• Examples
• Computing the homology of groups: the geometric way. Preprint. Joint work with J. Rubio.
• Homotopy groups of suspended classifying spaces: an experimental approach. Preprint. Joint work with J. Rubio.
  
• Lisp files
  
• OpenMath resolutions for some groups
• Examples

Effective homotopy

• Effective Homotopy of fibrations. Joint work with F. Sergeraert.
• Lisp files of the new module (together with the most recent version of Kenzo)
• Representation of central extensions

Persistent homology

• Lisp files

Digital images

• Repository of images

Generalized spectral sequences

• Lisp files. Joint work with A. Guidolin.

Multipersistence

• Lisp files. Joint work with A. Guidolin, J. Divasón and F. Vaccarino.

Serre spectral systems

• Lisp files. Joint work with A. Guidolin.

Eilenberg-Moore spectral sequence

• Lisp file. Joint work with J. Rubio, F. Sergeraert and M. Szymik.