Geodesic
Braid monodromy, orderings and transverse invariants
Plamenevskaya, Olga1
1 Department of Mathematics, Stony Brook University, Stony Brook, NY, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 6, pp. 3691-3718

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

A closed braid β naturally gives rise to a transverse link K in the standard contact 3–space. We study the effect of the dynamical properties of the monodromy of β, such as right-veering, on the contact-topological properties of K and the values of transverse invariants in Heegaard Floer and Khovanov homologies. Using grid diagrams and the structure of Dehornoy’s braid ordering, we show that θ̂(K) ∈HFK̂(m(K)) is nonzero whenever β has fractional Dehn twist coefficient C > 1. (For a 3–braid, we get a sharp result: θ̂≠0 if and only if the braid is right-veering.)

DOI : 10.2140/agt.2018.18.3691
Classification : 57M27, 57R17, 57R58
Keywords: Heegaard Floer transverse invariants, right-veering, fractional Dehn twist coefficient, grid diagrams

Plamenevskaya, Olga 1

1 Department of Mathematics, Stony Brook University, Stony Brook, NY, United States 
@article{10_2140_agt_2018_18_3691,
     author = {Plamenevskaya, Olga},
     title = {Braid monodromy, orderings and transverse invariants},
     journal = {Algebraic and Geometric Topology},
     pages = {3691--3718},
     publisher = {mathdoc},
     volume = {18},
     number = {6},
     year = {2018},
     doi = {10.2140/agt.2018.18.3691},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3691/}
}
TY  - JOUR
AU  - Plamenevskaya, Olga
TI  - Braid monodromy, orderings and transverse invariants
JO  - Algebraic and Geometric Topology
PY  - 2018
SP  - 3691
EP  - 3718
VL  - 18
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3691/
DO  - 10.2140/agt.2018.18.3691
ID  - 10_2140_agt_2018_18_3691
ER  - 
%0 Journal Article
%A Plamenevskaya, Olga
%T Braid monodromy, orderings and transverse invariants
%J Algebraic and Geometric Topology
%D 2018
%P 3691-3718
%V 18
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3691/
%R 10.2140/agt.2018.18.3691
%F 10_2140_agt_2018_18_3691
Plamenevskaya, Olga. Braid monodromy, orderings and transverse invariants. Algebraic and Geometric Topology, Tome 18 (2018) no. 6, pp. 3691-3718. doi: 10.2140/agt.2018.18.3691

Cité par Sources :