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Action of the Mazur pattern up to topological concordance

Alex Manchester

Algebraic & Geometric Topology 25 (2025) 2115–2142
Bibliography
1 A J Casson, C M Gordon, Cobordism of classical knots, from: "À la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 181 MR900252
2 J Cheeger, M Gromov, Bounds on the von Neumann dimension of L2-cohomology and the Gauss–Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985) 1 MR806699
3 T D Cochran, C W Davis, A Ray, Injectivity of satellite operators in knot concordance, J. Topol. 7 (2014) 948 MR3286894
4 T D Cochran, B D Franklin, M Hedden, P D Horn, Knot concordance and homology cobordism, Proc. Amer. Math. Soc. 141 (2013) 2193 MR3034445
5 T Cochran, S Friedl, P Teichner, New constructions of slice links, Comment. Math. Helv. 84 (2009) 617 MR2507256
6 T Cochran, S Harvey, The geometry of the knot concordance space, Algebr. Geom. Topol. 18 (2018) 2509 MR3848393
7 T D Cochran, S Harvey, P Horn, Filtering smooth concordance classes of topologically slice knots, Geom. Topol. 17 (2013) 2103 MR3109864
8 T D Cochran, S Harvey, C Leidy, Knot concordance and higher-order Blanchfield duality, Geom. Topol. 13 (2009) 1419 MR2496049
9 T D Cochran, S Harvey, C Leidy, Derivatives of knots and second-order signatures, Algebr. Geom. Topol. 10 (2010) 739 MR2606799
10 T D Cochran, S Harvey, C Leidy, Primary decomposition and the fractal nature of knot concordance, Math. Ann. 351 (2011) 443 MR2836668
11 T D Cochran, S Harvey, M Powell, Grope metrics on the knot concordance set, J. Topol. 10 (2017) 669 MR3665407
12 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and L2-signatures, Ann. of Math. 157 (2003) 433 MR1973052
13 M M Cohen, A course in simple-homotopy theory, Vol. 10, Springer (1973) MR362320
14 S Collins, Homology cobordism, smooth concordance, and the figure eight knot, preprint (2022) arXiv:2210.10308
15 A Conway, Homotopy ribbon discs with a fixed group, Algebr. Geom. Topol. 24 (2024) 4575 MR4843740
16 C W Davis, A Ray, Satellite operators as group actions on knot concordance, Algebr. Geom. Topol. 16 (2016) 945 MR3493412
17 M H Freedman, A new technique for the link slice problem, Invent. Math. 80 (1985) 453 MR791669
18 M H Freedman, F Quinn, Topology of 4-manifolds, 39, Princeton Univ. Press (1990) MR1201584
19 M H Freedman, P Teichner, 4-manifold topology, II : Dwyer’s filtration and surgery kernels, Invent. Math. 122 (1995) 531 MR1359603
20 S Friedl, P Teichner, New topologically slice knots, Geom. Topol. 9 (2005) 2129 MR2209368
21 R E Gompf, K Miyazaki, Some well-disguised ribbon knots, Topology Appl. 64 (1995) 117 MR1340864
22 R E Gompf, A I Stipsicz, 4-manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
23 M Hedden, J Pinzón-Caicedo, Satellites of infinite rank in the smooth concordance group, Invent. Math. 225 (2021) 131 MR4270665
24 A S Levine, Nonsurjective satellite operators and piecewise-linear concordance, Forum Math. Sigma 4 (2016) MR3589337
25 T Lidman, A N Miller, J Pinzón-Caicedo, Linking number obstructions to satellite homomorphisms, Quantum Topol. (2024)
26 R A Litherland, Cobordism of satellite knots, from: "Four-manifold theory" (editors C Gordon, R Kirby), Contemp. Math. 35, Amer. Math. Soc. (1984) 327 MR780587
27 R A Litherland, Symmetries of twist-spun knots, from: "Knot theory and manifolds" (editor D Rolfsen), Lecture Notes in Math. 1144, Springer (1985) 97 MR823283
28 C Livingston, P Melvin, Abelian invariants of satellite knots, from: "Geometry and topology" (editors J Alexander, J Harer), Lecture Notes in Math. 1167, Springer (1985) 217 MR827271
29 C Livingston, S Naik, Introduction to knot concordance, book project (2011)
30 A N Miller, Homomorphism obstructions for satellite maps, Trans. Amer. Math. Soc. Ser. B 10 (2023) 220 MR4545198
31 A N Miller, L Piccirillo, Knot traces and concordance, J. Topol. 11 (2018) 201 MR3784230
32 J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358 MR196736
33 A Ray, Satellite operators with distinct iterates in smooth concordance, Proc. Amer. Math. Soc. 143 (2015) 5005 MR3391056
34 H Seifert, On the homology invariants of knots, Quart. J. Math. Oxford Ser. 1 (1950) 23 MR35436
35 K Yasui, Corks, exotic 4-manifolds and knot concordance, preprint (2015) arXiv:1505.02551