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

Volume 23
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

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
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
A lower bound on the stable $4$–genus of knots

Damian Iltgen

Algebraic & Geometric Topology 22 (2022) 2239–2265
Bibliography
1 S Baader, L Lewark, The stable 4–genus of alternating knots, Asian J. Math. 21 (2017) 1183 MR3778124
2 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. XXXII, Amer. Math. Soc. (1978) 39 MR520521
3 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
4 A Conway, Algebraic concordance and Casson–Gordon invariants, technical note (2017)
5 A Conway, S Friedl, G Herrmann, Linking forms revisited, Pure Appl. Math. Q. 12 (2016) 493 MR3842851
6 C W Davis, Von Neumann rho invariants and torsion in the topological knot concordance group, Algebr. Geom. Topol. 12 (2012) 753 MR2914617
7 M H Freedman, The disk theorem for four-dimensional manifolds, from: "Proceedings of the International Congress of Mathematicians" (editors Z Ciesielski, C a Olech), PWN (1984) 647 MR804721
8 M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
9 P M Gilmer, On the slice genus of knots, Invent. Math. 66 (1982) 191 MR656619
10 P M Gilmer, Slice knots in S3, Quart. J. Math. Oxford Ser. 34 (1983) 305 MR711523
11 P Gilmer, Classical knot and link concordance, Comment. Math. Helv. 68 (1993) 1 MR1201199
12 S G Kim, Polynomial splittings of Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 138 (2005) 59 MR2127228
13 J Levine, Invariants of knot cobordism, Invent. Math. 8 (1969) 98 MR253348
14 P Lisca, Sums of lens spaces bounding rational balls, Algebr. Geom. Topol. 7 (2007) 2141 MR2366190
15 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
16 R A Litherland, Cobordism of satellite knots, from: "Four-manifold theory" (editors C Gordon, R Kirby), Contemp. Math., Amer. Math. Soc. (1984) 327 MR780587
17 C Livingston, The stable 4–genus of knots, Algebr. Geom. Topol. 10 (2010) 2191 MR2745668
18 C Livingston, S Naik, Introduction to knot concordance, work in progress
19 C Livingston, S Naik, Obstructing four-torsion in the classical knot concordance group, J. Differential Geom. 51 (1999) 1 MR1703602
20 C Livingston, S Naik, Knot concordance and torsion, Asian J. Math. 5 (2001) 161 MR1868169
21 K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR171275
22 S Naik, Casson–Gordon invariants of genus one knots and concordance to reverses, J. Knot Theory Ramifications 5 (1996) 661 MR1414093
23 P J Rippon, H Taylor, Even and odd periods in continued fractions of square roots, Fibonacci Quart. 42 (2004) 170 MR2071782
24 A Tamulis, Knots of ten or fewer crossings of algebraic order 2, J. Knot Theory Ramifications 11 (2002) 211 MR1895371
25 A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR248854