Volume 10, issue 2 (2010)

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

Volume 25
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

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
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
Triple point numbers of surface-links and symmetric quandle cocycle invariants

Kanako Oshiro

Algebraic & Geometric Topology 10 (2010) 853–865
Bibliography
1 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
2 J S Carter, M Saito, Knotted surfaces and their diagrams, Mathematical Surveys and Monographs 55, American Mathematical Society (1998) MR1487374
3 R Fenn, C Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992) 343 MR1194995
4 E Hatakenaka, An estimate of the triple point numbers of surface-knots by quandle cocycle invariants, Topology Appl. 139 (2004) 129 MR2051101
5 D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
6 S Kamada, Wirtinger presentations for higher-dimensional manifold knots obtained from diagrams, Fund. Math. 168 (2001) 105 MR1852735
7 S Kamada, Quandles with good involutions, their homologies and knot invariants, from: "Intelligence of low dimensional topology 2006", Ser. Knots Everything 40, World Sci. Publ., Hackensack, NJ (2007) 101 MR2371714
8 S Kamada, K Oshiro, Homology groups of symmetric quandles and cocycle invariants of links and surface-links, Trans. Amer. Math. Soc. (to appear)
9 A Kawauchi, On pseudo-ribbon surface-links, J. Knot Theory Ramifications 11 (2002) 1043 MR1941684
10 S V Matveev, Distributive groupoids in knot theory, Mat. Sb. $($N.S.$)$ 119(161) (1982) 78, 160 MR672410
11 D Roseman, Reidemeister-type moves for surfaces in four-dimensional space, from: "Knot theory (Warsaw, 1995)", Banach Center Publ. 42, Polish Acad. Sci. (1998) 347 MR1634466
12 S Satoh, Minimal triple point numbers of some non-orientable surface-links, Pacific J. Math. 197 (2001) 213 MR1810216
13 S Satoh, Non-additivity for triple point numbers on the connected sum of surface-knots, Proc. Amer. Math. Soc. 133 (2005) 613 MR2093086
14 S Satoh, A Shima, The 2–twist-spun trefoil has the triple point number four, Trans. Amer. Math. Soc. 356 (2004) 1007 MR1984465