Philippe Gaucher
Introduction
Contact : prénom.nom@irif.fr
Présentation : Mes travaux portent sur la topologie algébrique dirigée, qui se situe à l'interface entre les modèles géométriques de la concurrence (certains topologiques, d'autres combinatoires) et la topologie algébrique (CV en anglais). Les principaux modèles géométriques auxquels je m'intéresse sont plusieurs variantes des d-espaces de Grandis (multipointés ou non), les espaces de traces donnant lieu à des variantes semi-catégoriques appelées flot, les variantes de Moore de ces notions, et plusieurs améliorations de la notion d'ensemble précubique (ensemble transverse non symétrique et symétrique, ensemble précubique partiel).
Mots-clé : homotopie, catégorie, topologie, combinatoire, concurrence.
Présentation : Mes travaux portent sur la topologie algébrique dirigée, qui se situe à l'interface entre les modèles géométriques de la concurrence (certains topologiques, d'autres combinatoires) et la topologie algébrique (CV en anglais). Les principaux modèles géométriques auxquels je m'intéresse sont plusieurs variantes des d-espaces de Grandis (multipointés ou non), les espaces de traces donnant lieu à des variantes semi-catégoriques appelées flot, les variantes de Moore de ces notions, et plusieurs améliorations de la notion d'ensemble précubique (ensemble transverse non symétrique et symétrique, ensemble précubique partiel).
Mots-clé : homotopie, catégorie, topologie, combinatoire, concurrence.
Contact: firstname.lastname@irif.fr
Presentation: My work is about Directed Algebraic Topology, which is at the interface between the geometric models of concurrency (some of them topological, other ones combinatorial) and algebraic topology (CV in English). The main geometric models I am interested in are several variants of Grandis' d-spaces (multipointed or not), trace spaces giving rise to semicategorical variants called flow, Moore variants of these notions, and several improvements of the notion of precubical set (non-symmetric and symmetric transverse set, partial precubical set).
Keywords: homotopy, category, topology, combinatorics, concurrency.
Presentation: My work is about Directed Algebraic Topology, which is at the interface between the geometric models of concurrency (some of them topological, other ones combinatorial) and algebraic topology (CV in English). The main geometric models I am interested in are several variants of Grandis' d-spaces (multipointed or not), trace spaces giving rise to semicategorical variants called flow, Moore variants of these notions, and several improvements of the notion of precubical set (non-symmetric and symmetric transverse set, partial precubical set).
Keywords: homotopy, category, topology, combinatorics, concurrency.
Publications
- Directed paths and Moore flows, Rend. Mat. Appl. (7), Vol. 47 (2026), 201-210 (PDF)
- Branching spaces of multipointed d-spaces, to appear in Advanced Studies: Euro-Tbilisi Mathematical Journal (PDF)
- Branching spaces of multipointed d-spaces, à paraître dans Advanced Studies: Euro-Tbilisi Mathematical Journal (PDF)
- Towards a theory of natural directed paths, Compositionality, 7(6) 2025 (PDF)
- Globular subdivisions are dihomotopy equivalences, Bulletin of the Belgian Mathematical Society - Simon Stevin, 32(5) 607-656, 2025 (PDF)
- Natural homotopy of multipointed d-spaces, Mathematical Journal of Okayama University, (68) 13-62, 2026 (PDF)
- Homotopy theory of Moore flows (III), North-Western European Journal of Mathematics, No. 10, 55-113, 2024 (PDF)
- Directed degeneracy maps for precubical sets Theory and Applications of Categories, vol. 41, No. 7, 194-237, 2024 (PDF)
- Regular directed path and Moore flow, Rend. Mat. Appl. (7), Vol. 45 (1-2) (2024), 111-151 (PDF)
- Comparing cubical and globular directed paths, Fundamenta Mathematicae, 262 (2023), 259-286 (PDF)
- Comparing the non-unital and unital settings for directed homotopy, Cahiers de Topologie et Géométrie Différentielle Catégoriques, vol LXIV-2, Pages 176-197 (2023) (PDF)
- Homotopy theory of Moore flows (II), Extracta Mathematicae, vol. 36 (2), 157-239, 2021 (PDF)
- Homotopy theory of Moore flows (I), Compositionality, 3(3) 2021 (PDF)
- Left properness of flows, Theory and Applications of Categories, vol. 37, No. 19, 562-612, 2021 (PDF)
- Six model categories for directed homotopy, Categories and General Algebraic Structures with Applications, vol 15(1), 145-181, 2021 (PDF)
- Flows revisited: the model category structure and its left determinedness, Cahiers de Topologie et Géométrie Différentielle Catégoriques, vol LXI-2 (2020) (PDF)
- Enriched diagrams of topological spaces over locally contractible enriched categories, New-York Journal of Mathematics, 25 (2019), 1485–1510 (PDF)
- Combinatorics of past-similarity in higher dimensional transition systems, Theory and Applications of Categories, vol. 32, 1107-1164, 2017 (PDF)
- The choice of cofibrations of higher dimensional transition systems, New-York Journal of Mathematics, 21 (2015), 1117-1151 (PDF)
- Left determined model categories, New-York Journal of Mathematics, 21 (2015), 1093-1115 (PDF)
- The geometry of cubical and regular transition systems, Cahiers de Topologie et Géométrie Différentielle Catégoriques, vol LVI-4 (2015) (PDF)
- Erratum to ``Towards a homotopy theory of higher dimensional transition systems'', Theory and Applications of Categories, vol. 29, 17-20, 2014 (PDF)
- Homotopy Theory of Labelled Symmetric Precubical Sets, New-York Journal of Mathematics 20 (2014), 93-131 (PDF)
- Towards a homotopy theory of higher dimensional transition systems, Theory and Applications of Categories, vol. 25, 295-341, 2011 (PDF)
- Directed algebraic topology and higher dimensional transition systems, New-York Journal of Mathematics, 16 (2010), 409-461 (PDF)
- Combinatorics of labelling in higher dimensional automata, Theoretical Computer Science (2010), 411(11-13), pp 1452-1483 (PDF)
- Homotopical interpretation of globular complex by multipointed d-space, Theory and Applications of Categories, vol. 22, 588-621, 2009 (PDF)
- T-homotopy and refinement of observation (I) : Introduction, Electronic Notes in Theoretical Computer Sciences, 230 (2009), 103-110 (PDF)
- Towards a homotopy theory of process algebra, Homology, Homotopy and Applications, vol. 10 (1):p.353-388, 2008 (PDF)
- Globular realization and cubical underlying homotopy type of time flow of process algebra, New-York Journal of Mathematics, 14 (2008), 101-137 (PDF)
- T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences, Internat. J. Math. Math. Sci., Article ID 87404, 20 pages (2007) (PDF)
- T-homotopy and refinement of observation (III) : Invariance of the branching and merging homologies, New-York Journal of Mathematics, 12 (2006), 319-348 (PDF)
- T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type, New-York Journal of Mathematics, 12 (2006), 63-95 (PDF)
- Inverting weak dihomotopy equivalence using homotopy continuous flow, Theory and Applications of Categories, vol. 16, 59-83, 2006 (PDF)
- Flow does not model flows up to weak dihomotopy, Applied Categorical Structures, vol. 13, p. 371-388 (2005) (PDF)
- Homological properties of non-deterministic branchings and mergings in higher dimensional automata, Homology, Homotopy and Applications, vol. 7 (1):p.51-76, 2005 (PDF)
- Comparing globular complex and flow, New-York Journal of Mathematics 11 (2005), 97-150 (PDF)
- The homotopy branching space of a flow, Electronic Notes in Theoretical Computer Science vol. 100 : pp 95-109, 2004 (PDF)
- A model category for the homotopy theory of concurrency, Homology, Homotopy and Applications, vol. 5 (1):p.549-599, 2003 (PDF)
- Concurrent Process up to Homotopy (II), C. R. Acad. Sci. Paris Ser. I Math., 336(8):647-650, 2003 (French) (PDF)
- Concurrent Process up to Homotopy (I), C. R. Acad. Sci. Paris Ser. I Math., 336(7):593-596, 2003 (French) (PDF)
- (with Eric Goubault) Topological Deformation of Higher Dimensional Automata, Homology, Homotopy and Applications, vol. 5 (2):p.39-82, 2003 (PDF)
- (avec Eric Goubault) Topological Deformation of Higher Dimensional Automata, Homology, Homotopy and Applications, vol. 5 (2):p.39-82, 2003 (PDF)
- The branching nerve of HDA and the Kan condition, Theory and Applications of Categories 11 n°3 (2003), p.75-106 (PDF)
- Investigating The Algebraic Structure of Dihomotopy Types, Electronic Notes in Theoretical Computer Science, 52 (2) 2002 (PDF)
- About the globular homology of higher dimensional automata, Cahiers de Topologie et Géométrie Différentielle Catégoriques, p.107-156, vol XLIII-2 (2002) (PDF)
- Combinatorics of branchings in higher dimensional automata, Theory and Applications of Categories, 8 n°12 (2001), p.324-376 (PDF)
- From Concurrency to Algebraic Topology, Electronic Notes in Theoretical Computer Science, 39 (2000), no. 2, 19p (PDF)
- Homotopy invariants of higher dimensional categories and concurrency in computer science, Mathematical Structure in Computer Science, 10 (2000), no. 4, p.481-524 (PDF)
- Lambda-opérations sur l'homologie d'une algèbre de Lie de matrices, K-Theory, vol. 13(2), p.151-167, 1998 (PDF)
- Produit tensoriel de matrices, homologie cyclique, homologie des algèbres de Lie, Ann. Inst. Fourier (Grenoble), vol. 44(2), p.413-431, 1994 (PDF)
- Lambda-opérations et homologie des matrices, C. R. Acad. Sci. Paris Sér. I Math., 313(10):663-666, 1991 (PDF)
- Produit tensoriel de matrices et homologie cyclique, C. R. Acad. Sci. Paris Sér. I Math., 312(1):13-16, 1991 (PDF)
Autres écrits
Other writings
- Saturated directed spaces and generalized clocks (PDF)
- The homotopy types of directed path and trace spaces (PDF)
- The q-model category of multipointed d-spaces is not left proper (PDF)
- Left properness of Moore flows (PDF)
- The chain replacement of a poset flow (PDF)
- Branching spaces of transverse sets (PDF)
- Regular clock maps and trace spaces (PDF)
- Branching spaces of precubical sets (PDF)
- Corrections to the homotopy theory of Moore flows and its applications (PDF)
- Erratum to "Homotopy theory of Moore flows I" (PDF)
- About transfinite compositions of weak equivalences of higher dimensional transition systems (PDF)
- Closed symmetric monoidal structure and flow (PDF)
- Homotopical equivalence of combinatorial and categorical semantics of process algebra (PDF)
- Le Monopoly pour les nuls (PDF) avec le script PERL (TXT)
- Le Monopoly pour les nuls (PDF) avec le script PERL (TXT) (French)
Transcriptions en LaTeX
LaTeX transcriptions
- Compactly generated spaces (Gaunce Lewis) (PDF)
Profils
- zbMATH (Open Access) (HTML)
- Mathscinet (nécessite un abonnement) (HTML)
- ArXiv (HTML)
- Mathoverflow (HTML)
- ORCID (HTML)
- HAL-Science (HTML) : noter que cette base de donnée a des problèmes avec les homonymes et les mises à jour des prépublications
- Ne pas utiliser la base de données DBLP (HTML) : elle ne contient pas ou peu de références à mes publications, mais plutôt celles d'homonymes
Profiles
- zbMATH (Open Access) (HTML)
- Mathscinet (subscription required) (HTML)
- ArXiv (HTML)
- Mathoverflow (HTML)
- ORCID (HTML)
- HAL-Science (HTML): note that this database has signifiant issues with namesakes and updates of preprints
- Do not use the DBLB database (HTML): it contains few or no references to my publications, but rather those of namesakes
