Volume 15, issue 4 (2015)

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

Volume 21
Issue 2, 543–1074
Issue 1, 1–541

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
On the slice-ribbon conjecture for pretzel knots

Ana G Lecuona

Algebraic & Geometric Topology 15 (2015) 2133–2173
Bibliography
1 O Ahmadi, G Vega, On the parity of the number of irreducible factors of self-reciprocal polynomials over finite fields, Finite Fields Appl. 14 (2008) 124 MR2381481
2 R E Bedient, Double branched covers and pretzel knots, Pacific J. Math. 112 (1984) 265 MR743984
3 G Burde, H Zieschang, Knots, Studies in Math. 5, de Gruyter (2003) MR808776
4 A J Casson, C M Gordon, On slice knots in dimension three, from: "Algebraic and geometric topology" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 39 MR520521
5 A J Casson, C M Gordon, Cobordism of classical knots, from: "À la recherche de la topologie perdue", Progr. Math. 62, Birkhäuser (1986) 181 MR900252
6 D Cimasoni, V Florens, Generalized Seifert surfaces and signatures of colored links, Trans. Amer. Math. Soc. 360 (2008) 1223 MR2357695
7 S K Donaldson, The orientation of Yang–Mills moduli spaces and $4$–manifold topology, J. Differential Geom. 26 (1987) 397 MR910015
8 E Eftekhary, Heegaard Floer homologies for pretzel knots, arXiv:0311419v1
9 R H Fox, Some problems in knot theory, from: "Topology of $3$–manifolds and related topics", Prentice-Hall (1962) 168 MR0140100
10 R H Fox, J W Milnor, Singularities of $2$–spheres in $4$–space and cobordism of knots, Osaka J. Math. 3 (1966) 257 MR0211392
11 R E Gompf, A I Stipsicz, $4$–manifolds and Kirby calculus, Graduate Studies in Math. 20, Amer. Math. Soc. (1999) MR1707327
12 J Greene, S Jabuka, The slice-ribbon conjecture for $3$–stranded pretzel knots, Amer. J. Math. 133 (2011) 555 MR2808326
13 C Herald, P Kirk, C Livingston, Metabelian representations, twisted Alexander polynomials, knot slicing and mutation, Math. Z. 265 (2010) 925 MR2652542
14 S Jabuka, Rational Witt classes of pretzel knots, Osaka J. Math. 47 (2010) 977 MR2791566
15 P Kirk, C Livingston, Twisted Alexander invariants, Reidemeister torsion and Casson–Gordon invariants, Topology 38 (1999) 635 MR1670420
16 P Kirk, C Livingston, Twisted knot polynomials: Inversion, mutation and concordance, Topology 38 (1999) 663 MR1670424
17 J Levine, Invariants of knot cobordism, Invent. Math. 8 (1969) 98 MR0253348
18 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
19 P Lisca, Lens spaces, rational balls and the ribbon conjecture, Geom. Topol. 11 (2007) 429 MR2302495
20 P Lisca, Sums of lens spaces bounding rational balls, Algebr. Geom. Topol. 7 (2007) 2141 MR2366190
21 J M Montesinos, Seifert manifolds that are ramified two-sheeted cyclic coverings, Bol. Soc. Mat. Mexicana 18 (1973) 1 MR0341467
22 K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR0171275
23 W D Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc. 268 (1981) 299 MR632532
24 W D Neumann, F Raymond, Seifert manifolds, plumbing, $\mu $–invariant and orientation reversing maps, from: "Algebraic and geometric topology" (editor K C Millett), Lecture Notes in Math. 664, Springer (1978) 163 MR518415
25 P Ozsváth, Z Szabó, On the Floer homology of plumbed three-manifolds, Geom. Topol. 7 (2003) 185 MR1988284
26 R von Randow, Zur Topologie von dreidimensionalen Baummannigfaltigkeiten, Bonn. Math. Schr. No. 14 (1962) 131 MR0155304
27 K Reidemeister, Knotentheorie, Springer (1974) MR0345089
28 N Saveliev, A surgery formula for the $\bar\mu$–invariant, Topology Appl. 106 (2000) 91 MR1769335
29 H F Trotter, Noninvertible knots exist, Topology 2 (1963) 275 MR0158395