Algebraic & Geometric Topology Volume 16, issue 6 (2016)

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 length of a $3$–cocycle of the $5$–dihedral quandle

Shin Satoh

Algebraic & Geometric Topology 16 (2016) 3325–3359

DOI: 10.2140/agt.2016.16.3325

Bibliography

1	S Asami, S Satoh, An infinite family of noninvertible surfaces in 4–space, Bull. London Math. Soc. 37 (2005) 285 MR2119028
2	E Brieskorn, Automorphic sets and braids and singularities, from: "Braids" (editors J S Birman, A Libgober), Contemp. Math. 78, Amer. Math. Soc. (1988) 45 MR975077
3	J S Carter, D Jelsovsky, S Kamada, M Saito, Quandle homology groups, their Betti numbers, and virtual knots, J. Pure Appl. Algebra 157 (2001) 135 MR1812049
4	J S Carter, S Kamada, M Saito, Alexander numbering of knotted surface diagrams, Proc. Amer. Math. Soc. 128 (2000) 3761 MR1695171
5	R Fenn, C Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992) 343 MR1194995
6	R Fenn, C Rourke, B Sanderson, Trunks and classifying spaces, Appl. Categ. Structures 3 (1995) 321 MR1364012
7	R Fenn, C Rourke, B Sanderson, The rack space, Trans. Amer. Math. Soc. 359 (2007) 701 MR2255194
8	E Hatakenaka, An estimate of the triple point numbers of surface-knots by quandle cocycle invariants, Topology Appl. 139 (2004) 129 MR2051101
9	M Iwakiri, Calculation of dihedral quandle cocycle invariants of twist spun 2–bridge knots, J. Knot Theory Ramifications 14 (2005) 217 MR2128511
10	D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
11	S Kamada, K Oshiro, Homology groups of symmetric quandles and cocycle invariants of links and surface-links, Trans. Amer. Math. Soc. 362 (2010) 5501 MR2657689
12	S V Matveev, Distributive groupoids in knot theory, Mat. Sb. 119(161) (1982) 78, 160 MR672410
13	T Mochizuki, Some calculations of cohomology groups of finite Alexander quandles, J. Pure Appl. Algebra 179 (2003) 287 MR1960136
14	K Oshiro, Triple point numbers of surface-links and symmetric quandle cocycle invariants, Algebr. Geom. Topol. 10 (2010) 853 MR2629767
15	S Satoh, On non-orientable surfaces in 4–space which are projected with at most one triple point, Proc. Amer. Math. Soc. 128 (2000) 2789 MR1652241
16	S Satoh, Surface diagrams of twist-spun 2–knots, J. Knot Theory Ramifications 11 (2002) 413 MR1905695
17	S Satoh, No 2–knot has triple point number two or three, Osaka J. Math. 42 (2005) 543 MR2166721
18	S Satoh, A Shima, The 2–twist-spun trefoil has the triple point number four, Trans. Amer. Math. Soc. 356 (2004) 1007 MR1984465
19	S Satoh, A Shima, Triple point numbers and quandle cocycle invariants of knotted surfaces in 4–space, New Zealand J. Math. 34 (2005) 71 MR2141479
20	M Teragaito, Symmetry-spun tori in the four-sphere, from: "Knots 90" (editor A Kawauchi), de Gruyter (1992) 163 MR1177421
21	T Yajima, On simply knotted spheres in R⁴, Osaka J. Math. 1 (1964) 133 MR0172280
22	T Yashiro, Triple point numbers of twist spun knots, J. Knot Theory Ramifications 14 (2005) 831 MR2187599