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

Volume 26
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
An analogue of Milnor's invariants for knots in $3$–manifolds

Miriam Kuzbary

Algebraic & Geometric Topology 24 (2024) 3043–3067
Bibliography
1 A J Casson, Link cobordism and Milnor’s invariant, Bull. Lond. Math. Soc. 7 (1975) 39 MR0362286
2 D Celoria, On concordances in 3–manifolds, J. Topol. 11 (2018) 180 MR3784229
3 T D Cochran, Derivatives of links : Milnor’s concordance invariants and Massey’s products, 427, Amer. Math. Soc. (1990) MR1042041
4 T D Cochran, A Gerges, K Orr, Dehn surgery equivalence relations on 3–manifolds, Math. Proc. Cambridge Philos. Soc. 131 (2001) 97 MR1833077
5 T D Cochran, S Harvey, Homology and derived series of groups, II : Dwyer’s theorem, Geom. Topol. 12 (2008) 199 MR2377249
6 C W Davis, M Nagel, J Park, A Ray, Concordance of knots in S1 × S2, J. Lond. Math. Soc. 98 (2018) 59 MR3847232
7 W G Dwyer, Homology, Massey products and maps between groups, J. Pure Appl. Algebra 6 (1975) 177 MR0385851
8 R H Fox, J W Milnor, Singularities of 2–spheres in 4–space and cobordism of knots, Osaka Math. J. 3 (1966) 257 MR0211392
9 M H Freedman, P Teichner, 4–Manifold topology, II : Dwyer’s filtration and surgery kernels, Invent. Math. 122 (1995) 531 MR1359603
10 S Friedl, M Nagel, P Orson, M Powell, Satellites and concordance of knots in 3–manifolds, Trans. Amer. Math. Soc. 371 (2019) 2279 MR3896081
11 P Heck, Homotopy properties of knots in prime manifolds, preprint (2011) arXiv:1110.6903
12 J Hillman, Algebraic invariants of links, 52, World Sci. (2012) MR2931688
13 W Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935) 259 MR1512992
14 W Magnus, A Karrass, D Solitar, Combinatorial group theory: presentations of groups in terms of generators and relations, Interscience (1966) MR207802
15 D Miller, An extension of Milnor’s μ–invariants, Topology Appl. 65 (1995) 69 MR1354382
16 J Milnor, Link groups, Ann. of Math. 59 (1954) 177 MR0071020
17 J Milnor, Isotopy of links, from: "Algebraic geometry and topology" (editors R H Fox, D C Spencer, A W Tucker), Princeton Univ. Press (1957) 280 MR0092150
18 C A Otto, The (n)–solvable filtration of the link concordance group and Milnor’s μ–invariants, PhD thesis, Rice University (2011) MR2912159
19 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
20 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
21 R Porter, Milnor’s μ–invariants and Massey products, Trans. Amer. Math. Soc. 257 (1980) 39 MR0549154
22 R Schneiderman, Algebraic linking numbers of knots in 3–manifolds, Algebr. Geom. Topol. 3 (2003) 921 MR2012959
23 R Schneiderman, P Teichner, Higher order intersection numbers of 2–spheres in 4–manifolds, Algebr. Geom. Topol. 1 (2001) 1 MR1790501
24 J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170 MR0175956
25 D Stein, Massey products in the cohomology of groups with applications to link theory, Trans. Amer. Math. Soc. 318 (1990) 301 MR0958903
26 V G Turaev, Milnor invariants and Massey products, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 66 (1976) 189
27 E Z Yildiz, A note on knot concordance, Algebr. Geom. Topol. 18 (2018) 3119 MR3848410