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Operadic actions on long knots and $2$–string links

Etienne Batelier and Julien Ducoulombier

Algebraic & Geometric Topology 23 (2023) 833–882
Bibliography
1 M Aschenbrenner, S Friedl, H Wilton, 3–Manifold groups, Eur. Math. Soc. (2015) MR3444187
2 R Blair, J Burke, R Koytcheff, A prime decomposition theorem for the 2–string link monoid, J. Knot Theory Ramifications 24 (2015) 1550005 MR3334658
3 P Boavida de Brito, M Weiss, Manifold calculus and homotopy sheaves, Homology Homotopy Appl. 15 (2013) 361 MR3138384
4 R Budney, JSJ–decompositions of knot and link complements in S3, Enseign. Math. 52 (2006) 319 MR2300613
5 R Budney, Little cubes and long knots, Topology 46 (2007) 1 MR2288724
6 R Budney, An operad for splicing, J. Topol. 5 (2012) 945 MR3001316
7 R Budney, J Conant, R Koytcheff, D Sinha, Embedding calculus knot invariants are of finite type, Algebr. Geom. Topol. 17 (2017) 1701 MR3677937
8 J Burke, R Koytcheff, A colored operad for string link infection, Algebr. Geom. Topol. 15 (2015) 3371 MR3450765
9 J Cerf, Topologie de certains espaces de plongements, Bull. Soc. Math. France 89 (1961) 227 MR140120
10 P R Cromwell, Knots and links, Cambridge Univ. Press (2004) MR2107964
11 J Ducoulombier, D Kosanovic, On the 𝒞2–algebra structure of long knots, in preparation
12 T G Goodwillie, M Weiss, Embeddings from the point of view of immersion theory, II, Geom. Topol. 3 (1999) 103 MR1694808
13 A E Hatcher, A proof of the Smale conjecture, Diff(S3) O(4), Ann. of Math. 117 (1983) 553 MR701256
14 A E Hatcher, Spaces of incompressible surfaces, technical note (1999)
15 A E Hatcher, Notes on basic 3–manifold topology, course notes (2007)
16 A Hatcher, D McCullough, Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds, Geom. Topol. 1 (1997) 91 MR1486644
17 M W Hirsch, Differential topology, 33, Springer (1994) MR1336822
18 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
19 W Jaco, P B Shalen, A new decomposition theorem for irreducible sufficiently-large 3–manifolds, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 71 MR520524
20 K Johannson, Homotopy equivalences of 3–manifolds with boundaries, 761, Springer (1979) MR551744
21 J Kalliongis, D McCullough, Fiber-preserving diffeomorphisms and imbeddings, preprint (1998) arXiv:9802003
22 A Kupers, Lectures on diffeomorphism groups of manifolds, (2019)
23 W Magnus, A Karrass, D Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Dover (2004) MR2109550
24 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
25 B A Munson, I Volić, Cosimplicial models for spaces of links, J. Homotopy Relat. Struct. 9 (2014) 419 MR3258688
26 R S Palais, Local triviality of the restriction map for embeddings, Comment. Math. Helv. 34 (1960) 305 MR123338
27 R S Palais, Homotopy theory of infinite dimensional manifolds, Topology 5 (1966) 1 MR189028
28 H Schubert, Die eindeutige Zerlegbarkeit eines Knotens in Primknoten, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1949 (1949) 57 MR0031733
29 D P Sinha, Operads and knot spaces, J. Amer. Math. Soc. 19 (2006) 461 MR2188133
30 N E Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967) 133 MR210075
31 W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357 MR648524
32 I Volić, Finite type knot invariants and the calculus of functors, Compos. Math. 142 (2006) 222 MR2197410
33 F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR224099
34 M Weiss, Embeddings from the point of view of immersion theory, I, Geom. Topol. 3 (1999) 67 MR1694812
35 D Yau, Colored operads, 170, Amer. Math. Soc. (2016) MR3444662