Volume 26, issue 1 (2022)

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

Volume 26
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Abelian quotients of the $Y$–filtration on the homology cylinders via the LMO functor

Yuta Nozaki, Masatoshi Sato and Masaaki Suzuki

Geometry & Topology 26 (2022) 221–282
DOI: 10.2140/gt.2022.26.221
Bibliography
1 B Bollobás, Graph theory: an introductory course, 63, Springer (1979) MR536131
2 D Cheptea, K Habiro, G Massuyeau, A functorial LMO invariant for Lagrangian cobordisms, Geom. Topol. 12 (2008) 1091 MR2403806
3 S Chmutov, S Duzhin, J Mostovoy, Introduction to Vassiliev knot invariants, Cambridge Univ. Press (2012) MR2962302
4 J Conant, R Schneiderman, P Teichner, Tree homology and a conjecture of Levine, Geom. Topol. 16 (2012) 555 MR2916294
5 J Conant, R Schneiderman, P Teichner, Whitney tower concordance of classical links, Geom. Topol. 16 (2012) 1419 MR2967057
6 J Conant, R Schneiderman, P Teichner, Geometric filtrations of string links and homology cylinders, Quantum Topol. 7 (2016) 281 MR3459962
7 S Garoufalidis, M Goussarov, M Polyak, Calculus of clovers and finite type invariants of 3–manifolds, Geom. Topol. 5 (2001) 75 MR1812435
8 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
9 M Goussarov, Finite type invariants and n–equivalence of 3–manifolds, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 517 MR1715131
10 M N Gusarov, Variations of knotted graphs : the geometric technique of n–equivalence, Algebra i Analiz 12 (2000) 79 MR1793618
11 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
12 K Habiro, G Massuyeau, Symplectic Jacobi diagrams and the Lie algebra of homology cylinders, J. Topol. 2 (2009) 527 MR2546585
13 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
14 R Hain, Infinitesimal presentations of the Torelli groups, J. Amer. Math. Soc. 10 (1997) 597 MR1431828
15 A Heap, Bordism invariants of the mapping class group, Topology 45 (2006) 851 MR2248515
16 D Johnson, The structure of the Torelli group, III : The abelianization of 𝒯 , Topology 24 (1985) 127 MR793179
17 J Levine, Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243 MR1823501
18 J Levine, Addendum and correction to “Homology cylinders : an enlargement of the mapping class group”, Algebr. Geom. Topol. 2 (2002) 1197 MR1943338
19 J Levine, Labeled binary planar trees and quasi-Lie algebras, Algebr. Geom. Topol. 6 (2006) 935 MR2240921
20 G Massuyeau, Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant, Bull. Soc. Math. France 140 (2012) 101 MR2903772
21 G Massuyeau, J B Meilhan, Characterization of Y 2–equivalence for homology cylinders, J. Knot Theory Ramifications 12 (2003) 493 MR1985907
22 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
23 J B Meilhan, On surgery along Brunnian links in 3–manifolds, Algebr. Geom. Topol. 6 (2006) 2417 MR2286031
24 S Morita, Casson’s invariant for homology 3–spheres and characteristic classes of surface bundles, I, Topology 28 (1989) 305 MR1014464
25 S Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699 MR1224104
26 S Morita, Structure of the mapping class groups of surfaces: a survey and a prospect, from: "Proceedings of the Kirbyfest" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2, Geom. Topol. Publ. (1999) 349 MR1734418
27 S Morita, T Sakasai, M Suzuki, Torelli group, Johnson kernel, and invariants of homology spheres, Quantum Topol. 11 (2020) 379 MR4118638
28 T Ohtsuki, Quantum invariants : a study of knots, 3–manifolds, and their sets, 29, World Sci. (2002) MR1881401
29 J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170 MR175956