Algebraic & Geometric Topology Volume 21, issue 2 (2021)

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Generalized Dehn twists on surfaces and homology cylinders

Yusuke Kuno and Gwénaël Massuyeau

Algebraic & Geometric Topology 21 (2021) 697–754

DOI: 10.2140/agt.2021.21.697

Bibliography

1	A Alekseev, N Kawazumi, Y Kuno, F Naef, The Goldman–Turaev Lie bialgebra in genus zero and the Kashiwara–Vergne problem, Adv. Math. 326 (2018) 1 MR3758425
2	A Alekseev, Y Kosmann-Schwarzbach, E Meinrenken, Quasi-Poisson manifolds, Canad. J. Math. 54 (2002) 3 MR1880957
3	D Cheptea, K Habiro, G Massuyeau, A functorial LMO invariant for Lagrangian cobordisms, Geom. Topol. 12 (2008) 1091 MR2403806
4	T D Cochran, Derivatives of links : Milnor’s concordance invariants and Massey’s products, 427, Amer. Math. Soc. (1990) MR1042041
5	T D Cochran, k–cobordism for links in S³, Trans. Amer. Math. Soc. 327 (1991) 641 MR1055569
6	T D Cochran, A Gerges, K Orr, Dehn surgery equivalence relations on 3–manifolds, Math. Proc. Cambridge Philos. Soc. 131 (2001) 97 MR1833077
7	J Conant, R Schneiderman, P Teichner, Geometric filtrations of string links and homology cylinders, Quantum Topol. 7 (2016) 281 MR3459962
8	S Garoufalidis, J Levine, Finite type 3–manifold invariants, the mapping class group and blinks, J. Differential Geom. 47 (1997) 257 MR1601612
9	S Garoufalidis, J Levine, Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphism, from: "Graphs and patterns in mathematics and theoretical physics" (editors M Lyubich, L Takhtajan), Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 173 MR2131016
10	W M Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986) 263 MR846929
11	N Habegger, Milnor, Johnson, and tree level perturbative invariants, preprint (2000)
12	N Habegger, X S Lin, On link concordance and Milnor’s μ invariants, Bull. Lond. Math. Soc. 30 (1998) 419 MR1620841
13	N Habegger, G Masbaum, The Kontsevich integral and Milnor’s invariants, Topology 39 (2000) 1253 MR1783857
14	N Habegger, W Pitsch, Tree level Lie algebra structures of perturbative invariants, J. Knot Theory Ramifications 12 (2003) 333 MR1983089
15	K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
16	K Habiro, G Massuyeau, From mapping class groups to monoids of homology cobordisms: a survey, from: "Handbook of Teichmüller theory, III" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 17, Eur. Math. Soc. (2012) 465 MR2952770
17	A Heap, Bordism invariants of the mapping class group, Topology 45 (2006) 851 MR2248515
18	S A Jennings, The group ring of a class of infinite nilpotent groups, Canad. J. Math. 7 (1955) 169 MR68540
19	D Johnson, An abelian quotient of the mapping class group ℐ_g, Math. Ann. 249 (1980) 225 MR579103
20	D Johnson, A survey of the Torelli group, from: "Low-dimensional topology" (editor S J Lomonaco Jr.), Contemp. Math. 20, Amer. Math. Soc. (1983) 165 MR718141
21	M I Kargapolov, J I Merzljakov, Fundamentals of the theory of groups, 62, Springer (1979) MR551207
22	N Kawazumi, Cohomological aspects of Magnus expansions, preprint (2005) arXiv:math/0505497
23	N Kawazumi, Y Kuno, The logarithms of Dehn twists, Quantum Topol. 5 (2014) 347 MR3283405
24	N Kawazumi, Y Kuno, Intersection of curves on surfaces and their applications to mapping class groups, Ann. Inst. Fourier (Grenoble) 65 (2015) 2711 MR3449595
25	N Kawazumi, Y Kuno, The Goldman–Turaev Lie bialgebra and the Johnson homomorphisms, from: "Handbook of Teichmüller theory, V" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 26, Eur. Math. Soc. (2016) 97 MR3497295
26	Y Kuno, A combinatorial construction of symplectic expansions, Proc. Amer. Math. Soc. 140 (2012) 1075 MR2869092
27	Y Kuno, The generalized Dehn twist along a figure eight, J. Topol. Anal. 5 (2013) 271 MR3096306
28	J Levine, Labeled binary planar trees and quasi-Lie algebras, Algebr. Geom. Topol. 6 (2006) 935 MR2240921
29	G Massuyeau, Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant, Bull. Soc. Math. France 140 (2012) 101 MR2903772
30	G Massuyeau, Formal descriptions of Turaev’s loop operations, Quantum Topol. 9 (2018) 39 MR3760878
31	G Massuyeau, J B Meilhan, Equivalence relations for homology cylinders and the core of the Casson invariant, Trans. Amer. Math. Soc. 365 (2013) 5431 MR3074379
32	G Massuyeau, V Turaev, Fox pairings and generalized Dehn twists, Ann. Inst. Fourier (Grenoble) 63 (2013) 2403 MR3237452
33	G Massuyeau, V Turaev, Quasi-Poisson structures on representation spaces of surfaces, Int. Math. Res. Not. 2014 (2014) 1 MR3158528
34	S Morita, Casson’s invariant for homology 3–spheres and characteristic classes of surface bundles, I, Topology 28 (1989) 305 MR1014464
35	S Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699 MR1224104
36	K E Orr, Homotopy invariants of links, Invent. Math. 95 (1989) 379 MR974908
37	D Quillen, Rational homotopy theory, Ann. of Math. 90 (1969) 205 MR258031
38	T Sakasai, Homology cylinders and the acyclic closure of a free group, Algebr. Geom. Topol. 6 (2006) 603 MR2220691
39	T Satoh, A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics, from: "Handbook of Teichmüller theory, V" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 26, Eur. Math. Soc. (2016) 167 MR3497296
40	J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170 MR175956
41	V G Turaev, Intersections of loops in two-dimensional manifolds, Mat. Sb. 106(148) (1978) 566 MR507817
42	V G Turaev, Nilpotent homotopy types of closed 3–manifolds, from: "Topology" (editors L D Faddeev, A A Malcev), Lecture Notes in Math. 1060, Springer (1984) 355 MR770255
43	M Van den Bergh, Double Poisson algebras, Trans. Amer. Math. Soc. 360 (2008) 5711 MR2425689