Algebraic & Geometric Topology Volume 15, issue 2 (2015)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Positive quandle homology and its applications in knot theory

Zhiyun Cheng and Hongzhu Gao

Algebraic & Geometric Topology 15 (2015) 933–963

DOI: 10.2140/agt.2015.15.933

Bibliography

1	J S Carter, A survey of quandle ideas, from: "Introductory lectures on knot theory" (editors L H Kauffman, S Lambropoulou, S Jablan, J H Przytycki), Ser. Knots Everything 46, World Sci. Publ. (2012) 22 MR2885229
2	J S Carter, M Elhamdadi, M Saito, Twisted quandle homology theory and cocycle knot invariants, Algebr. Geom. Topol. 2 (2002) 95 MR1885217
3	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
4	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
5	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
6	J S Carter, M Saito, Canceling branch points on projections of surfaces in $4$–space, Proc. Amer. Math. Soc. 116 (1992) 229 MR1126191
7	J S Carter, M Saito, Knotted surfaces and their diagrams, Math. Surveys and Monographs 55, Amer. Math. Soc. (1998) MR1487374
8	S Carter, S Kamada, M Saito, Surfaces in $4$–space, Encyclopaedia of Math. Sciences 142, Springer (2004) MR2060067
9	W E Clark, M Elhamdadi, M Saito, T Yeatman, Quandle colorings of knots and applications, J. Knot Theory Ramifications 23 (2014) 1450035, 29 MR3253967
10	M Eisermann, The number of knot group representations is not a Vassiliev invariant, Proc. Amer. Math. Soc. 128 (2000) 1555 MR1657727
11	R Fenn, C Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992) 343 MR1194995
12	R Fenn, C Rourke, B Sanderson, Trunks and classifying spaces, Appl. Categ. Structures 3 (1995) 321 MR1364012
13	R Fenn, C Rourke, B Sanderson, James bundles, Proc. London Math. Soc. 89 (2004) 217 MR2063665
14	R H Fox, A quick trip through knot theory, from: "Topology of $3$–manifolds and related topics" (editor M K Fort Jr.), Prentice-Hall (1962) 120 MR0140099
15	C A Giller, Towards a classical knot theory for surfaces in $\mathbb{R}^{4}$, Illinois J. Math. 26 (1982) 591 MR674227
16	F Harary, L H Kauffman, Knots and graphs, I: Arc graphs and colorings, Adv. in Appl. Math. 22 (1999) 312 MR1675756
17	B Ho, S Nelson, Matrices and finite quandles, Homology Homotopy Appl. 7 (2005) 197 MR2175299
18	A Inoue, Quasitriviality of quandles for link-homotopy, J. Knot Theory Ramifications 22 (2013) 1350026, 10 MR3070837
19	A Inoue, Y Kabaya, Quandle homology and complex volume, Geom. Dedicata 171 (2014) 265 MR3226796
20	D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
21	S Kamada, Knot invariants derived from quandles and racks, from: "Invariants of knots and $3$–manifolds", Geom. Topol. Monogr. 4 (2002) 103 MR2002606
22	S Kamada, V Lebed, K Tanaka, The shadow nature of positive and twisted quandle cocycle invariants of knots, (2014) arXiv:1409.4072v2
23	R A Litherland, S Nelson, The Betti numbers of some finite racks, J. Pure Appl. Algebra 178 (2003) 187 MR1952425
24	T W Mattman, P Solis, A proof of the Kauffman–Harary conjecture, Algebr. Geom. Topol. 9 (2009) 2027 MR2550465
25	S V Matveev, Distributive groupoids in knot theory, Mat. Sb. 119(161) (1982) 78, 160 MR672410
26	T Mochizuki, Some calculations of cohomology groups of finite Alexander quandles, J. Pure Appl. Algebra 179 (2003) 287 MR1960136
27	M Niebrzydowski, J H Przytycki, Homology of dihedral quandles, J. Pure Appl. Algebra 213 (2009) 742 MR2494367
28	M Polyak, Minimal generating sets of Reidemeister moves, Quantum Topol. 1 (2010) 399 MR2733246
29	J H Przytycki, $3$–coloring and other elementary invariants of knots, from: "Knot theory" (editors V F R Jones, J Kania-Bartoszyńska, J H Przytycki, V G Traczyk Pawełand Turaev), Banach Center Publ. 42, Polish Acad. Sci., Warsaw (1998) 275 MR1634462
30	J H Przytycki, Distributivity versus associativity in the homology theory of algebraic structures, Demonstratio Math. 44 (2011) 823 MR2906433
31	J H Przytycki, A S Sikora, Distributive products and their homology, Comm. Algebra 42 (2014) 1258 MR3169627
32	D Rolfsen, Knots and links, Math. Lecture Series 7, Publish or Perish (1976) MR0515288
33	D Roseman, Reidemeister-type moves for surfaces in four-dimensional space, from: "Knot theory" (editors V F R Jones, J Kania-Bartoszyńska, J H Przytycki, V G Traczyk Pawełand Turaev), Banach Center Publ. 42, Polish Acad. Sci. (1998) 347 MR1634466
34	C Rourke, B Sanderson, There are two $2$–twist-spun trefoils, (2002) arXiv:math.GT/0006062
35	S Satoh, A Shima, The $2$–twist-spun trefoil has the triple point number four, Trans. Amer. Math. Soc. 356 (2004) 1007 MR1984465
36	M Takasaki, Abstraction of symmetric transformations, Tôhoku Math. J. 49 (1943) 145 MR0021002
37	L Vendramin, On the classification of quandles of low order, J. Knot Theory Ramifications 21 (2012) MR2926571