Geodesic
Signed ordered knotlike quandle presentations
Nelson, Sam1
1University of California, Riverside, 900 University Avenue, Riverside CA 92521, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 443-462
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We define enhanced presentations of quandles via generators and relations with additional information comprising signed operations and an order structure on the set of generators. Such a presentation determines a virtual link diagram up to virtual moves. We list formal Reidemeister moves in which Tietze moves on the presented quandle are accompanied by corresponding changes to the order structure. Omitting the order structure corresponds to replacing virtual isotopy by welded isotopy.

DOI : 10.2140/agt.2005.5.443
Keywords: quandles, virtual knots, presentations, Reidemeister moves, welded isotopy

Nelson, Sam  1

1 University of California, Riverside, 900 University Avenue, Riverside CA 92521, USA 
@article{10_2140_agt_2005_5_443,
     author = {Nelson, Sam},
     title = {Signed ordered knotlike quandle presentations},
     journal = {Algebraic and Geometric Topology},
     pages = {443--462},
     year = {2005},
     volume = {5},
     number = {2},
     doi = {10.2140/agt.2005.5.443},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.443/}
}
TY  - JOUR
AU  - Nelson, Sam
TI  - Signed ordered knotlike quandle presentations
JO  - Algebraic and Geometric Topology
PY  - 2005
SP  - 443
EP  - 462
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.443/
DO  - 10.2140/agt.2005.5.443
ID  - 10_2140_agt_2005_5_443
ER  - 
%0 Journal Article
%A Nelson, Sam
%T Signed ordered knotlike quandle presentations
%J Algebraic and Geometric Topology
%D 2005
%P 443-462
%V 5
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.443/
%R 10.2140/agt.2005.5.443
%F 10_2140_agt_2005_5_443
Nelson, Sam. Signed ordered knotlike quandle presentations. Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 443-462. doi: 10.2140/agt.2005.5.443

[1] J S Carter, D Jelsovsky, S Kamada, L Langford, M Saito, State-sum invariants of knotted curves and surfaces from quandle cohomology, Electron. Res. Announc. Amer. Math. Soc. 5 (1999) 146

[2] J S Carter, S Kamada, M Saito, Stable equivalence of knots on surfaces and virtual knot cobordisms, J. Knot Theory Ramifications 11 (2002) 311

[3] H A Dye, Virtual knots undetected by 1– and 2–strand bracket polynomials, Topology Appl. 153 (2005) 141

[4] R Fenn, M Jordan-Santana, L Kauffman, Biquandles and virtual links, Topology Appl. 145 (2004) 157

[5] R Fenn, R Rimányi, C Rourke, The braid-permutation group, Topology 36 (1997) 123

[6] R Fenn, C Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992) 343

[7] R Fenn, C Rourke, B Sanderson, Trunks and classifying spaces, Appl. Categ. Structures 3 (1995) 321

[8] R Fenn, C Rourke, B Sanderson, The rack space, Trans. Amer. Math. Soc. 359 (2007) 701

[9] M Goussarov, M Polyak, O Viro, Finite-type invariants of classical and virtual knots, Topology 39 (2000) 1045

[10] D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37

[11] L H Kauffman, Virtual knot theory, European J. Combin. 20 (1999) 663

[12] G Kuperberg, What is a virtual link?, Algebr. Geom. Topol. 3 (2003) 587

Cité par Sources :