Geodesic
Knot and braid invariants from contact homology II
Ng, Lenhard1
1 Department of Mathematics, Stanford University, Stanford, California 94305, USA
Geometry & topology, Tome 9 (2005) no. 3, pp. 1603-1637.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We present a topological interpretation of knot and braid contact homology in degree zero, in terms of cords and skein relations. This interpretation allows us to extend the knot invariant to embedded graphs and higher-dimensional knots. We calculate the knot invariant for two-bridge knots and relate it to double branched covers for general knots. In the appendix we show that the cord ring is determined by the fundamental group and peripheral structure of a knot and give applications.

DOI : 10.2140/gt.2005.9.1603
Keywords: contact homology, knot invariant, differential graded algebra, skein relation, character variety

Ng, Lenhard 1

1 Department of Mathematics, Stanford University, Stanford, California 94305, USA 
@article{GT_2005_9_3_a9,
     author = {Ng, Lenhard},
     title = {Knot and braid invariants from contact homology {II}},
     journal = {Geometry & topology},
     pages = {1603--1637},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2005},
     doi = {10.2140/gt.2005.9.1603},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.1603/}
}
TY  - JOUR
AU  - Ng, Lenhard
TI  - Knot and braid invariants from contact homology II
JO  - Geometry & topology
PY  - 2005
SP  - 1603
EP  - 1637
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.1603/
DO  - 10.2140/gt.2005.9.1603
ID  - GT_2005_9_3_a9
ER  - 
%0 Journal Article
%A Ng, Lenhard
%T Knot and braid invariants from contact homology II
%J Geometry & topology
%D 2005
%P 1603-1637
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.1603/
%R 10.2140/gt.2005.9.1603
%F GT_2005_9_3_a9
Ng, Lenhard. Knot and braid invariants from contact homology II. Geometry & topology, Tome 9 (2005) no. 3, pp. 1603-1637. doi : 10.2140/gt.2005.9.1603. http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.1603/

[1] A Abbondandolo, M Schwarz, On the Floer homology of cotangent bundles, Comm. Pure Appl. Math. 59 (2006) 254

[2] S J Bigelow, Braid groups are linear, J. Amer. Math. Soc. 14 (2001) 471

[3] J S Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press (1974)

[4] S P Humphries, An approach to automorphisms of free groups and braids via transvections, Math. Z. 209 (1992) 131

[5] D Krammer, The braid group $B_4$ is linear, Invent. Math. 142 (2000) 451

[6] W Magnus, Rings of Fricke characters and automorphism groups of free groups, Math. Z. 170 (1980) 91

[7] L Ng, Knot and braid invariants from contact homology I, Geom. Topol. 9 (2005) 247

[8] D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976)

[9] D A Salamon, J Weber, Floer homology and the heat flow, Geom. Funct. Anal. 16 (2006) 1050

[10] C Viterbo, Functors and computations in Floer homology with applications II, preprint (1998)

Cité par Sources :