Algebraic & Geometric Topology Volume 22, issue 2 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

The topological slice genus of satellite knots

Peter Feller, Allison N Miller and Juanita Pinzón-Caicedo

Algebraic & Geometric Topology 22 (2022) 709–738

DOI: 10.2140/agt.2022.22.709

Bibliography

1	S Baader, P Feller, L Lewark, L Liechti, On the topological 4–genus of torus knots, Trans. Amer. Math. Soc. 370 (2018) 2639 MR3748580
2	R C Blanchfield, Intersection theory of manifolds with operators with applications to knot theory, Ann. of Math. 65 (1957) 340 MR85512
3	A J Casson, C M Gordon, On slice knots in dimension three, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math., 32, Amer. Math. Soc. (1978) 39 MR520521
4	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
5	J C Cha, A N Miller, M Powell, Two-solvable and two-bipolar knots with large four-genera, Math. Res. Lett. 28 (2021) 331 MR4258974
6	T Cochran, S Harvey, The geometry of the knot concordance space, Algebr. Geom. Topol. 18 (2018) 2509 MR3848393
7	P Feller, L Lewark, On classical upper bounds for slice genera, Selecta Math. 24 (2018) 4885 MR3874707
8	P Feller, L Lewark, Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space, preprint (2019) arXiv:1905.08305
9	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
10	S Friedl, M Powell, A calculation of Blanchfield pairings of 3–manifolds and knots, Mosc. Math. J. 17 (2017) 59 MR3634521
11	P M Gilmer, On the slice genus of knots, Invent. Math. 66 (1982) 191 MR656619
12	R E Gompf, A I Stipsicz, 4–Manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
13	J Hom, Bordered Heegaard Floer homology and the tau-invariant of cable knots, J. Topol. 7 (2014) 287 MR3217622
14	C Kearton, Cobordism of knots and Blanchfield duality, J. Lond. Math. Soc. 10 (1975) 406 MR385873
15	K H Ko, A Seifert-matrix interpretation of Cappell and Shaneson’s approach to link cobordisms, Math. Proc. Cambridge Philos. Soc. 106 (1989) 531 MR1010376
16	A S Levine, Nonsurjective satellite operators and piecewise-linear concordance, Forum Math. Sigma 4 (2016) MR3589337
17	J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR246314
18	W B R Lickorish, An introduction to knot theory, 175, Springer (1997) MR1472978
19	R A Litherland, Signatures of iterated torus knots, from: "Topology of low-dimensional manifolds" (editor R A Fenn), Lecture Notes in Math. 722, Springer (1979) 71 MR547456
20	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
21	C Livingston, Knot 4–genus and the rank of classes in W(ℚ(t)), Pacific J. Math. 252 (2011) 113 MR2862144
22	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
23	D McCoy, Null homologous twisting and the algebraic genus, from: "2019–10 MATRIX annals" (editors D R Wood, J de Grier, C E Praeger, T Tao), MATRIX Book Ser. 4, Springer (2021) 147
24	A N Miller, Winding number m and −m patterns acting on concordance, Proc. Amer. Math. Soc. 147 (2019) 2723 MR3951445
25	L Rudolph, Some topologically locally-flat surfaces in the complex projective plane, Comment. Math. Helv. 59 (1984) 592 MR780078
26	L Rudolph, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. 29 (1993) 51 MR1193540
27	L Rudolph, Quasipositive plumbing (constructions of quasipositive knots and links, V), Proc. Amer. Math. Soc. 126 (1998) 257 MR1452826
28	H Schubert, Knoten und Vollringe, Acta Math. 90 (1953) 131 MR72482
29	L R Taylor, On the genera of knots, from: "Topology of low-dimensional manifolds" (editor R A Fenn), Lecture Notes in Math. 722, Springer (1979) 144 MR547461
30	A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR248854