2004/09/01 by Tamás Kálmán, Kálmán, Tamás
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.math/0409005
32 pages
arxiv created 2004/09/01 · arxiv updated 2009/12/01
We compute the Chekanov-Eliashberg contact homology of what we call the Legendrian closure of a positive braid. We also construct an augmentation for each such link diagram. Then we apply the monodromy techniques established in an earlier paper to a certain natural loop in the space L' of positive Legendrian (p,q) torus knots to show that L' has a nontrivial fundamental group, which is mapped non-injectively into the fundamental group of K by the map induced by inclusion (here, K is the space of all smooth positive (p,q) torus knots). This is the first example that Legendrian and classical knots behave differently at the level of one parameter families.