Thèse et habilitation
[PhD]
Algèbres de Hopf graduées et fibrés plats sur les 3-variétés,
Thèse de Doctorat (2001),
pdf.
[HdR]
Quantum invariants of 3-manifolds, TQFTs, and Hopf monads, Habilitation à Diriger des Recherches (2010),
pdf.
Publications
[1]
Hopf group-coalgebras,
J. Pure Appl. Algebra 171, (2002), 75-122,
pdf.
[2]
Involutory Hopf group-coalgebras and flat bundles over 3-manifolds,
Fund. Math. 188 (2005), 241-270,
pdf.
[3]
Graded quantum groups and quasitriangular Hopf group-coalgebras,
Comm. Algebra 33 (2005), 3029-3050,
pdf.
[4]
Hopf diagrams and quantum invariants (avec A. Bruguières),
Algebr. Geom. Topol. 4 (2005), 1677-1710,
pdf.
[5]
Kirby elements and quantum invariants,
Proc. London Math. Soc. 93 (2006), 474-514,
pdf.
[6]
Hopf monads (avec A. Bruguières),
Advances in Math. 215 (2007), 679-733,
pdf.
[7]
Categorical centers and Reshetikhin-Turaev invariants (avec A. Bruguières),
Act. Math. Viet. 33 (2008), 255-277,
pdf.
[8] Deux appendices :
Algebraic properties of Hopf G-coalgebras (
pdf) et
Invariants of 3-dimensional G-manifolds from Hopf coalgebras (
pdf), dans le livre
Homotopy Quantum Field Theory (
pdf),
Tracts in Mathematics 10, (2010), 236-262.
[9]
Quantum double of Hopf monads and categorical centers (avec A. Bruguières),
Trans. Am. Math. Soc. 364 (2012), 1225-1279,
pdf.
[10]
Hopf monads on monoidal categories (avec A. Bruguières et S. Lack),
Advances in Math. 227 (2011), 745-800,
pdf.
[11]
Traces on ideals in pivotal categories (avec N. Geer et B. Patureau-Mirand),
Quantum Topol. 4 (2013), 91-124,
pdf.
[12]
On 3-dimensional Homotopy Quantum Field Theory, Part I (avec V. Turaev),
Int. J. Math. 23 (2012), 01-28,
pdf.
[13]
On the center of fusion categories (avec A. Bruguières),
Pacific J. Math. 264 (2013), 1-30,
pdf.
[14]
On the graded center of graded categories (avec V. Turaev),
J. Pure Appl. Algebra 217 (2013), 1895-1941,
pdf.
[15]
The doubles of a braided Hopf algebra (avec A. Bruguières),
Contemp. Math. 585 (2013), 175-197,
pdf.
[16]
On 3-dimensional Homotopy Quantum Field Theory II: The surgery approach (avec V. Turaev),
Int. J. Math. 25 (2014), 1-66,
pdf.
[17]
Monoidal Categories and Topological Field Theory (avec V. Turaev), livre de la série
Progress in Mathematics, Vol. 322 (2017), Birkhauser, 523 pages,
flyer.
Monograph recipient of the 2016 Ferran Sunyer i Balaguer Prize.
[18]
Generalized Kuperberg invariants of 3-manifolds (avec R. Kashaev),
Algebr. Geom. Topol. 19 (2019), 2575–2624,
pdf.
[19]
On 3-dimensional Homotopy Quantum Field Theory III: Comparison of two approaches (avec V. Turaev),
Int. J. Math. 31 (2020), 1-57,
pdf.
[20]
Monoidal categories graded by crossed modules and 3-dimensional HQFTs (avec K. Sozer),
Advances in Math. 428 (2023), 109155,
pdf.
[21]
Non compact (2+1)-TQFTs from non-semisimple spherical categories (avec F. Costantino, N. Geer, et B. Patureau-Mirand), preprint
arXiv:2302.04509 (2023),
pdf.
[22]
Chromatic maps for finite tensor categories (avec F. Costantino, N. Geer, et B. Patureau-Mirand), preprint
arXiv:2305.14626 (2023),
pdf.
[23]
Hopf crossed module (co)algebras (avec K. Sozer), preprint
arXiv:2305.15485 (2023),
pdf.
[24]
3d TQFTs and 3-manifold invariants (avec K. Sozer), preprint
arXiv:2401.10587 (2024), to appear in the 2nd Edition of Encyclopedia of Mathematical Physics,
pdf.
En préparation
- Crossed extensions of graded fusion categories (avec K. Sozer)
- State sum invariants of combed 3-manifolds (avec G. Calimici)
- Monoidal categories graded by topological groups