Algebraic Topology

We study effective methods in algebraic topology, with a view towards the computation of normal forms or bases, and the construction of small resolutions of various algebraic structures: monoids and groups, algebras and operads, categories and higher structures, etc. The construction methods can come from combinatorial group theory (rewriting, Garside structures), combinatorial algebra (Gröbner bases), or homological algebra (Koszul duality, Morse theory). We explore potential deep foundational connexions between these different points of view, to unify, generalise and improve them.

Related Publications

  • [DOI] Y. Guiraud, E. Hoffbeck, and P. Malbos, “Convergent presentations and polygraphic resolutions of associative algebras,” Math. z., vol. 293, iss. 1-2, p. 113–179, 2019.
    [Bibtex] 
    @article{GuiraudHoffbeckMalbos19,
AUTHOR = {Guiraud, Yves and Hoffbeck, Eric and Malbos, Philippe},
TITLE = {Convergent presentations and polygraphic resolutions of
associative algebras},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {293},
YEAR = {2019},
NUMBER = {1-2},
PAGES = {113--179},
ISSN = {0025-5874},
MRCLASS = {18G10 (16S37 16Z05 18N10 68Q42)},
MRNUMBER = {4002273},
MRREVIEWER = {Hayrullah Ay\i k},
DOI = {10.1007/s00209-018-2185-z},
URL = {https://doi.org/10.1007/s00209-018-2185-z},
}
  • [PDF] Y. Guiraud, “Rewriting methods in higher algebra,” Habilitation à diriger des recherches PhD Thesis, 2019.
    [Bibtex] 
    @phdthesis{Guiraud19,
TITLE = {{Rewriting methods in higher algebra}},
AUTHOR = {Guiraud, Yves},
URL = {https://hal.archives-ouvertes.fr/tel-02161197},
SCHOOL = {{Universit{\'e} Paris 7}},
YEAR = {2019},
MONTH = Jun,
KEYWORDS = {Higher category ; Polygraph ; Rewriting ; Squier's theorem ; Homotopy ; Homology ; Monoid ; Artin monoid ; Associative algebra ; Cat{\'e}gorie sup{\'e}rieure ; Polygraphe ; R{\'e}{\'e}criture ; Th{\'e}or{\`e}me de Squier ; Homotopie ; Homologie ; Coh{\'e}rence ; R{\'e}solution ; Mono{\"i}de ; Mono{\"i}de d'Artin ; Alg{\`e}bre associative},
TYPE = {Habilitation {\`a} diriger des recherches},
PDF = {https://hal.archives-ouvertes.fr/tel-02161197/file/hdr.pdf},
HAL_ID = {tel-02161197},
HAL_VERSION = {v1},
}
  • [DOI] Y. Guiraud and P. Malbos, “Polygraphs of finite derivation type,” Math. structures comput. sci., vol. 28, iss. 2, p. 155–201, 2018.
    [Bibtex] 
    @article{GuiraudMalbos18,
author = {Guiraud, Yves and Malbos, Philippe},
doi = {10.1017/S0960129516000220},
fjournal = {Mathematical Structures in Computer Science. A Journal in the Applications of Categorical, Algebraic and Geometric Methods in Computer Science},
issn = {0960-1295},
journal = {Math. Structures Comput. Sci.},
mrclass = {18B40 (16S15 20F10 68Q42)},
mrnumber = {3742562},
mrreviewer = {Eylem G\"uzel Karpuz},
number = {2},
pages = {155--201},
title = {Polygraphs of finite derivation type},
url = {https://doi.org/10.1017/S0960129516000220},
volume = {28},
year = {2018},
}
  • P. Dehornoy and Y. Guiraud, “Quadratic normalisation in monoids,” Internat. j. algebra comput., vol. 26, iss. 5, p. 935–972, 2016.
    [Bibtex] 
    @article{DehornoyGuiraud16,
author = {Dehornoy, Patrick and Guiraud, Yves},
journal = {Internat. J. Algebra Comput.},
number = {5},
pages = {935--972},
title = {Quadratic normalisation in monoids},
volume = {26},
year = {2016},
}
  • [DOI] S. Gaussent, Y. Guiraud, and P. Malbos, “Coherent presentations of artin monoids,” Compos. math., vol. 151, p. 957–998, 2015.
    [Bibtex] 
    @article{GaussentGuiraudMalbos15,
author = {Gaussent, Stéphane and Guiraud, Yves and Malbos, Philippe},
doi = {10.1112/S0010437X14007842},
fjournal = {Compositio Mathematica},
issn = {1570-5846},
issue = {5},
journal = {Compos. Math.},
pages = {957--998},
title = {Coherent presentations of Artin monoids},
volume = {151},
year = {2015},
}
  • Y. Guiraud, P. Malbos, and S. Mimram, “A homotopical completion procedure with applications to coherence of monoids,” in 24th international conference on rewriting techniques and applications (rta 2013), 2013, p. 223–238.
    [Bibtex] 
    @inproceedings{GuiraudMalbosMimram13,
author = {Guiraud, Yves and Malbos, Philippe and Mimram, Samuel},
booktitle = {24th International Conference on Rewriting Techniques and Applications (RTA 2013)},
pages = {223--238},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
title = {A homotopical completion procedure with applications to coherence of monoids},
volume = {21},
year = {2013},
}
  • [DOI] Y. Guiraud and P. Malbos, “Higher-dimensional normalisation strategies for acyclicity,” Adv. math., vol. 231, iss. 3-4, p. 2294–2351, 2012.
    [Bibtex] 
    @article{GuiraudMalbos12advances,
author = {Guiraud, Yves and Malbos, Philippe},
coden = {ADMTA4},
doi = {10.1016/j.aim.2012.05.010},
fjournal = {Advances in Mathematics},
issn = {0001-8708},
journal = {Adv. Math.},
mrclass = {Preliminary Data},
mrnumber = {2964639},
number = {3-4},
pages = {2294--2351},
title = {Higher-dimensional normalisation strategies for acyclicity},
url = {http://dx.doi.org/10.1016/j.aim.2012.05.010},
volume = {231},
year = {2012},
}
  • Y. Guiraud and P. Malbos, “Coherence in monoidal track categories,” Math. structures comput. sci., vol. 22, iss. 6, p. 931–969, 2012.
    [Bibtex] 
    @article{GuiraudMalbos12mscs,
author = {Guiraud, Yves and Malbos, Philippe},
fjournal = {Mathematical Structures in Computer Science},
journal = {Math. Structures Comput. Sci.},
number = {6},
pages = {931--969},
title = {Coherence in Monoidal Track Categories},
volume = {22},
year = {2012},
}
  • Y. Guiraud and P. Malbos, “Identities among relations for higher-dimensional rewriting systems,” S?min. congr., vol. 26, p. 145–161, 2011.
    [Bibtex] 
    @article{GuiraudMalbos11,
author = {Guiraud, Yves and Malbos, Philippe},
fjournal = {Séminaires et Congrès},
journal = {Sémin. Congr.},
pages = {145--161},
title = {Identities among relations for higher-dimensional rewriting systems},
volume = {26},
year = {2011},
}
  • Y. Guiraud and P. Malbos, “Higher-dimensional categories with finite derivation type,” Theory appl. categ., vol. 22, iss. 18, p. 420–478, 2009.
    [Bibtex] 
    @article{GuiraudMalbos09,
author = {Guiraud, Yves and Malbos, Philippe},
fjournal = {Theory and Applications of Categories},
issn = {1201-561X},
journal = {Theory Appl. Categ.},
mrclass = {18C10 (18D05 18D10 57M20)},
mrnumber = {2559651 (2010j:18006)},
mrreviewer = {R. H. Street},
number = {18},
pages = {420--478},
title = {Higher-dimensional categories with finite derivation type},
volume = {22},
year = {2009},
}

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