No Access

COLORING INVARIANTS OF SPATIAL GRAPHS

MACIEJ NIEBRZYDOWSKI

Department of Mathematics, University of Louisiana at Lafayette, 1403 Johnston Street, 217 Maxim D. Doucet Hall, Lafayette, LA 70504-1010, USA

Search for more papers by this author

https://doi.org/10.1142/S0218216510008169Cited by:2 (Source: Crossref)

Abstract

We define the fundamental quandle of a spatial graph and several invariants derived from it. In the category of graph tangles, we define an invariant based on the walks in the graph and cocycles from nonabelian quandle cohomology.

Keywords:

AMSC: 05C10, 57M27

References

N. Andruskiewitsch and M. Graña, Adv. Math. 178, 177 (2003), DOI: 10.1016/S0001-8708(02)00071-3. Crossref, Web of Science, Google Scholar
J. S. Carteret al., Osaka J. Math. 42, 499 (2005). Web of Science, Google Scholar
J. S. Carter , S. Kamada and M. Saito , Encyclopaedia of Mathematical Sciences, Low-Dimensional Topology III , eds. R. Gamkrelidze and V. Vassiliev ( Springer , 2004 ) . Google Scholar
R. Fenn and C. Rourke, J. Knot Theory Ramifications 1, 343 (1992), DOI: 10.1142/S0218216592000203. Link, Google Scholar
T. Fleming and B. Mellor, Kobe J. Math. 24, 57 (2007). Google Scholar
R. H. Fox, A quick trip through knot theory, Top. 3-Manifolds, Proc. 1961 Top. Inst. Univ. Georgia, ed. M. K. Fort Jr (Princeton-Hall, Englewood Cliffs. NJ, 1962) pp. 120–167. Google Scholar
The GAP Group, GAP — Groups, Algorithms, and Programming, http://www.gap-system.org . Google Scholar
A. Ishii, Algebr. Geom. Topol. 8, 1403 (2008), DOI: 10.2140/agt.2008.8.1403. Crossref, Web of Science, Google Scholar
A. Ishii and M. Iwakiri, Quandle cocycle invariants for spatial graphs and knotted handlebodies, preprint (2008) . Google Scholar
Y. Ishii and A. Yasuhara, J. Knot Theory Ramifications 6, 319 (1997), DOI: 10.1142/S0218216597000224. Link, Web of Science, Google Scholar
D. Joyce, J. Pure Appl. Algebra 23, 37 (1982), DOI: 10.1016/0022-4049(82)90077-9. Crossref, Web of Science, Google Scholar
S. Kamada, Intelligence of Low Dimensional Topology 2006, eds. S. Carteret al. (World Scientific Publishing Co., 2007) pp. 101–108. Link, Google Scholar
L. H. Kauffman, Trans. Amer. Math. Soc. 311, 697 (1989). Crossref, Web of Science, Google Scholar
J. McAtee, D. Silver and S. Williams, J. Knot Theory Ramifications 10, 109 (2001), DOI: 10.1142/S0218216501000755. Link, Web of Science, Google Scholar
M. Niebrzydowski, J. Knot Theory Ramifications 15, 1049 (2006), DOI: 10.1142/S0218216506004932. Link, Web of Science, Google Scholar