Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Noncommutative divergence and the Turaev cobracket

Toyo Taniguchi

Algebraic & Geometric Topology 25 (2025) 3103–3132
Bibliography
1 A Alekseev, N Kawazumi, Y Kuno, F Naef, The Goldman–Turaev Lie bialgebra and the Kashiwara–Vergne problem in higher genera, preprint (2018) arXiv:1804.09566
2 M Chas, Combinatorial Lie bialgebras of curves on surfaces, Topology 43 (2004) 543 MR2041630
3 J Cuntz, D Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995) 251 MR1303029
4 N Enomoto, T Satoh, New series in the Johnson cokernels of the mapping class groups of surfaces, Algebr. Geom. Topol. 14 (2014) 627 MR3159965
5 V Ginzburg, Lectures on noncommutative geometry, preprint (2005) arXiv:math/0506603
6 A Hattori, Rank element of a projective module, Nagoya Math. J. 25 (1965) 113 MR175950
7 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
8 M Kontsevich, Y Soibelman, Notes on A-algebras, A-categories and non-commutative geometry, from: "Homological mirror symmetry" (editors A Kapustin, M Kreuzer, K G Schlesinger), Lecture Notes in Phys. 757, Springer (2009) 153 MR2596638
9 S Lazzarini, T Masson, Connections on Lie algebroids and on derivation-based noncommutative geometry, J. Geom. Phys. 62 (2012) 387 MR2864487
10 R C Lyndon, Cohomology theory of groups with a single defining relation, Ann. of Math. 52 (1950) 650 MR47046
11 G Massuyeau, Formal descriptions of Turaev’s loop operations, Quantum Topol. 9 (2018) 39 MR3760878
12 G Massuyeau, T Sakasai, Morita’s trace maps on the group of homology cobordisms, J. Topol. Anal. 12 (2020) 775 MR4139214
13 S Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699 MR1224104
14 G Powell, On derivations of free algebras over operads and the generalized divergence, preprint (2021) arXiv:2105.09123
15 T Satoh, On the lower central series of the IA-automorphism group of a free group, J. Pure Appl. Algebra 216 (2012) 709 MR2864772
16 J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170 MR175956
17 V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. 24 (1991) 635 MR1142906
18 D Vaintrob, The string topology BV algebra, Hochschild cohomology and the Goldman bracket on surfaces, preprint (2007) arXiv:math/0702859
19 M Vaintrob, A relationship between Hochschild cohomology and the Goldman bracket for compact oriented two-dimensional manifolds, preprint (2007)
20 P Xu, Gerstenhaber algebras and BV-algebras in Poisson geometry, Comm. Math. Phys. 200 (1999) 545 MR1675117
21 K Yano, E M Patterson, Horizontal lifts from a manifold to its cotangent bundle, J. Math. Soc. Japan 19 (1967) 185 MR212724
22 P Zusmanovich, On Lie p-algebras of cohomological dimension one, Indag. Math. 30 (2019) 288 MR3912595