Homepage of Gwénaël Massuyeau

Research papers

[30] with K. Habiro, The Johnson-Morita theory for the handlebody group. Preprint (2024), 62 pages.

[29] with Q. Faes, On the non-triviality of the torsion subgroup of the abelianized Johnson kernel. Preprint (2022), 31 pages, to appear in Ann. Inst. Fourier.

[28] with D. Moussard, A splicing formula for the LMO invariant. Canad. J. Math. 73:6 (2021) 1743-1770.

[27] with Y. Kuno, Generalized Dehn twists on surfaces and homology cylinders. Algebr. Geom. Topol. 21 (2021) 697-754.

[26] with K. Habiro, Generalized Johnson homomorphisms for extended N-series. J. Algebra 510 (2018) 205-258.

[25] with K. Habiro, The Kontsevich integral for bottom tangles in handlebodies. Quantum Topol. 12:4 (2021) 593-703.

[24] with T. Sakasai, Morita's trace maps on the group of homology cobordisms. J. Topol. Anal. 12:3 (2020) 775-818.

[23] with V. Florens and J. Serrano de Rodrigo, A functorial extension of the Magnus representation to the category of three-dimensional cobordisms. Fund. Math. 240 (2018) 221-263.

[22] Formal descriptions of Turaev's loop operations. Quantum Topol. 9 (2018) 39-117.

[21] with V. Turaev, Brackets in representation algebras of Hopf algebras. J. Noncomm. Geom. 12:2 (2018) 577-636.

[20] with V. Florens, A functorial extension of the abelian Reidemeister torsions of three-manifolds. Enseign. Math. 61:1/2 (2015) 161-210.

[19] Splitting formulas for the LMO invariant of rational homology three-spheres. Algebr. Geom. Topol. 14:6 (2014) 3553-3588.

[18] with V. Turaev, Brackets in the Pontryagin algebras of manifolds. Mém. Soc. Math. France 154 (2017), 138 pages.

[17] with V. Turaev, Quasi-Poisson structures on representation spaces of surfaces. Int. Math. Res. Not. 2014:1 (2014) 1-64.

[16] with V. Turaev, Fox pairings and generalized Dehn twists. Ann. Inst. Fourier 63:6 (2013) 2403-2456.

[15] with J.-B. Meilhan, Equivalence relations for homology cylinders and the core of the Casson invariant. Trans. Amer. Math. Soc. 365:10 (2013) 5431-5502.

[14] with A. Oancea and D. Salamon, Lefschetz fibrations, intersection numbers, and representations of the framed braid group. Bull. Math. Soc. Sci. Math. Roumanie 56(104):4 (2013) 435-486.

[13] Canonical extensions of Morita homomorphisms to the Ptolemy groupoid. Geom. Dedicata 158:1 (2012) 365-395.

[12] Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant. Bull. Soc. Math. France 140:1 (2012) 101-161.

[11] with K. Habiro, Symplectic Jacobi diagrams and the Lie algebra of homology cylinders. J. Topology 2:3 (2009) 527-569.

[10] with D. Cheptea and K. Habiro, A functorial LMO invariant for Lagrangian cobordisms. Geom. Topol. 12 (2008) 1091-1170.

[9] Finite-type invariants of three-manifolds and the dimension subgroup problem. J. London Math. Soc. 75:3 (2007) 791-811.

[8] Some finiteness properties for the Reidemeister-Turaev torsion of three-manifolds. J. Knot Th. Ramifications 19:3 (2010) 405-447.

[7] with F. Nichita, Yang-Baxter operators arising from algebra structures and the Alexander polynomial of knots. Comm. Algebra 33:7 (2005) 2375-2385.

[6] Cohomology rings, Rochlin function, linking pairing and the Goussarov-Habiro theory of three-manifolds. Algebr. Geom. Topol. 3 (2003) 1139-1166.

[5] with F. Deloup, Quadratic functions and complex spin structures on 3-manifolds. Topology 44:3 (2005) 509-555.

[4] with F. Deloup, Quadratic functions on torsion groups. J. Pure Applied Algebra 198:1-3 (2005) 105-121.

[3] with F. Deloup, Reidemeister-Turaev torsion modulo one of rational homology three-spheres. Geom. Topol. 7 (2003) 773-787.

[2] with J.-B. Meilhan, Characterization of Y_2-equivalence for homology cylinders. J. Knot Th. Ramifications 12:4 (2003) 493-522.

[1] Spin Borromean surgeries. Trans. Amer. Math. Soc. 355:10 (2003) 3991-4017.

Expository papers

[d] Surgery equivalence relations for 3-manifolds. Winter Braids Lecture Notes, Tome 8 (2021), Exposé no. 1, 41 pages.

[c] with Y. Kuno and S. Tsuji, Generalized Dehn twists in low-dimensional topology. Topology and Geometry: A Collection of Essays Dedicated to Vladimir G. Turaev, 357-398. Ed. A. Papadopoulos, IRMA Lect. Math. Theor. Phys. 33, Eur. Math. Soc., Berlin, 2021.

[b] with K. Habiro, From mapping class groups to monoids of homology cobordisms: a survey. Handbook of Teichmüller theory, Volume III, 465-529. Ed. A. Papadopoulos, IRMA Lect. Math. Theor. Phys. 17, Eur. Math. Soc., Zürich, 2012.

[a] An introduction to the abelian Reidemeister torsion of three-dimensional manifolds. Ann. Math. Blaise Pascal 18:1 (2011) 61-140. (Notes of a mini-course given at "Tresses in Pau" in October 2009.)

Dissertations

[ii] Some aspects of the theory of finite-type invariants in three-dimensional topology. H.D.R. dissertation, University of Strasbourg, 2012.

[i] Finite type invariants of three-dimensional manifolds and spin structures. Ph.D. dissertation, University of Nantes, 2002.

Other texts

[β] Commentaire : Ω_3=0 chez René Thom. Oeuvres mathématiques de René Thom. Volume I, 93-94. Documents Math., 15, Soc. Math. France, Paris, 2017.

[α] Equivalence relations on three-dimensional manifolds defined by subgroups of the Torelli group & the core of the Casson invariant. Oberwolfach Reports 7:4 (2010) 3147-3149. (Short report on the paper [15] with J.-B. Meilhan.)

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