arXiv subjects

Olga Plamenevskaya

Publications and source records attributed to Olga Plamenevskaya.

22 records · Page 2Linked to original sources

arXiv2004

Transverse knots and Khovanov homology

We define an invariant of transverse links in the standard contact 3-sphere as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives a bound on the self-linking number in terms of Rasmussen's invariant s(K). We prove that our invariant vanishes for transverse knot stabilizations, and that it is non-zero for quasipositive braids. We also discuss a connection to Heegaard Floer invariants.

math.GT↗

arXiv2004

Bounds for the Thurston-Bennequin number from Floer homology

Using a knot concordance invariant from the Heegaard Floer theory of Ozsvath and Szabo, we obtain new bounds for the Thurston-Bennequin and rotation numbers of Legendrian knots in S^3. We also apply these bounds to calculate the knot concordance invariant for certain knots.

math.SG↗

arXiv2003

Contact Structures with Distinct Heegaard Floer Invariants

We prove that the contact structures on Y= dX induced by non-homotopic Stein structures on the 4-manifold X have distinct Heegaard Floer invariants.

math.SG↗

arXiv1999

A Residue Formula for SU(2)-valued Moment Maps

Jeffrey and Kirwan suggested expressions for intersection pairings on the reduced space of a Hamiltonian G-space in terms of multiple residues. In this paper we prove a residue formula for symplectic volumes of reduced spaces of a quasi-Hamiltonian SU(2)-space. The definition of quasi-Hamiltonian G-spaces was recently introduced by Alekseev, Malkin and Meinrenken.

math.DG↗