The Group of Contactomorphisms of the Sphere Fixing an Overtwisted Disk
We calculate the weak homotopy type of the group of contactomorphisms of the three-sphere which coincide with the identity on (a neighborhood of) an overtwisted disk.
math.GT↗
arXiv subjects
Katarzyna Dymara
Publications and source records attributed to Katarzyna Dymara.
Legendrian knots in overtwisted contact structures
We prove that two Legendrian knots in a contact structure which is trivializable as a plane bundle are Legendrian isotopic provided that (1) they are isotopic as framed knots, (2) they have the same rotation number with respect to some parallelization of the contact structure, and (3) there is an overtwisted disk disjoint with both knots. (For zero-homologous knots the condition (1) reads as: (1a) they are isotopic as topological knots, and (1b) they have the same Thurston-Bennequin invariant.) Then we discuss the situation when condition (3) is not fulfilled, in particular that of non-loose Legendrian knots.
math.GT↗