Volume 11, issue 3 (2011)

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

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

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

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Surface links which are coverings over the standard torus

Inasa Nakamura

Algebraic & Geometric Topology 11 (2011) 1497–1540
Bibliography
1 E Artin, Theory of braids, Ann. of Math. $(2)$ 48 (1947) 101 MR0019087
2 S Asami, S Satoh, An infinite family of non-invertible surfaces in $4$–space, Bull. London Math. Soc. 37 (2005) 285 MR2119028
3 I Berstein, A L Edmonds, On the construction of branched coverings of low-dimensional manifolds, Trans. Amer. Math. Soc. 247 (1979) 87 MR517687
4 I Berstein, A L Edmonds, On the classification of generic branched coverings of surfaces, Illinois J. Math. 28 (1984) 64 MR730712
5 J S Birman, Braids, links, and mapping class groups, Annals of Math. Studies 82, Princeton Univ. Press (1974) MR0375281
6 O Bogopolski, Introduction to group theory, EMS Textbooks in Math., European Math. Soc. (2008) MR2396717
7 J Boyle, Classifying $1$–handles attached to knotted surfaces, Trans. Amer. Math. Soc. 306 (1988) 475 MR933302
8 J Boyle, The turned torus knot in $S^4$, J. Knot Theory Ramifications 2 (1993) 239 MR1238874
9 G Burde, K Murasugi, Links and Seifert fiber spaces, Duke Math. J. 37 (1970) 89 MR0253313
10 G Burde, H Zieschang, Eine Kennzeichnung der Torusknoten, Math. Ann. 167 (1966) 169 MR0210113
11 J S Carter, D Jelsovsky, S Kamada, L Langford, M Saito, Quandle cohomology and state-sum invariants of knotted curves and surfaces, Trans. Amer. Math. Soc. 355 (2003) 3947 MR1990571
12 J S Carter, D Jelsovsky, S Kamada, M Saito, Computations of quandle cocycle invariants of knotted curves and surfaces, Adv. Math. 157 (2001) 36 MR1808844
13 J S Carter, S Kamada, M Saito, Geometric interpretations of quandle homology, J. Knot Theory Ramifications 10 (2001) 345 MR1825963
14 J S Carter, M Saito, Knotted surfaces and their diagrams, Math. Surveys and Monogr. 55, Amer. Math. Soc. (1998) MR1487374
15 E Fadell, L Neuwirth, Configuration spaces, Math. Scand. 10 (1962) 111 MR0141126
16 H Gluck, The embedding of two-spheres in the four-sphere, Trans. Amer. Math. Soc. 104 (1962) 308 MR0146807
17 J Hillman, $2$–knots and their groups, Australian Math. Soc. Lecture Ser. 5, Cambridge Univ. Press (1989) MR1001757
18 M W Hirsch, Differential topology, Graduate Texts in Math. 33, Springer (1994) MR1336822
19 D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
20 S Kamada, Surfaces in $\mathbf{R}^4$ of braid index three are ribbon, J. Knot Theory Ramifications 1 (1992) 137 MR1164113
21 S Kamada, $2$–dimensional braids and chart descriptions, from: "Topics in knot theory (Erzurum, 1992)" (editor M E Bozhuyuk), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 399, Kluwer (1993) 277 MR1257915
22 S Kamada, A characterization of groups of closed orientable surfaces in $4$–space, Topology 33 (1994) 113 MR1259518
23 S Kamada, An observation of surface braids via chart description, J. Knot Theory Ramifications 5 (1996) 517 MR1406718
24 S Kamada, Braid and knot theory in dimension four, Math. Surveys and Monogr. 95, Amer. Math. Soc. (2002) MR1900979
25 R A Litherland, Symmetries of twist-spun knots, from: "Knot theory and manifolds (Vancouver, B.C., 1983)" (editor D Rolfsen), Lecture Notes in Math. 1144, Springer (1985) 97 MR823283
26 C Livingston, Stably irreducible surfaces in $S^4$, Pacific J. Math. 116 (1985) 77 MR769824
27 T Mochizuki, Some calculations of cohomology groups of finite Alexander quandles, J. Pure Appl. Algebra 179 (2003) 287 MR1960136
28 J M Montesinos, On twins in the four-sphere. I, Quart. J. Math. Oxford Ser. $(2)$ 34 (1983) 171 MR698205
29 H Neumann, Generalized free products with amalgamated subgroups. II, Amer. J. Math. 71 (1949) 491 MR0030522
30 L Rudolph, Braided surfaces and Seifert ribbons for closed braids, Comment. Math. Helv. 58 (1983) 1 MR699004
31 M Teragaito, Symmetry-spun tori in the four-sphere, from: "Knots 90 (Osaka, 1990)" (editor A Kawauchi), de Gruyter (1992) 163 MR1177421
32 T Yanagawa, On ribbon $2$–knots: The $3$-manifold bounded by the $2$–knots, Osaka J. Math. 6 (1969) 447 MR0266193