Holomorphic discs and surgery exact triangles.

Authors: Bijan Sahamie
Subjects: Geometric Topology
link: http://arxiv.org/abs/1002.4141
Abstract

We show a connection between the surgery exact sequence in knot Floer
homology and the sequence derived in [15]. As a result we may interpret the
maps \Gamma_1 and \Gamma_2 from [15] as counting small holomorphic triangles in
a suitable Heegaard triple diagram. Consequently, the exact sequence in [15]
also works with coherent orientations and admits refinements with respect to
Spinc structures. The vanishing results of the contact element from [15] thus
generalize to \Z-coefficients. Finally, we derive a surgery exact triangle
using maps defined by counting holomorphic discs instead of triangles.