Bijan Sahamie
Holomorphic discs and surgery exact triangles.
Tue, 02/23/2010 - 16:01 — SomNambulAuthors: Bijan Sahamie
Subjects: Geometric Topology
AbstractWe 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.Dehn Twists in Heegaard Floer Homology.
Wed, 08/26/2009 - 14:58 — SomNambulAuthors: Bijan Sahamie
Subjects: Geometric Topology
AbstractWe derive a new exact sequence in the hat-version of Heegaard Floer homology.
As a consequence we see a functorial connection between the invariant of
Legendrian knots and the contact element. As an application we derive two
vanishing results of the contact element making it possible to easily read off
its vanishing out of a surgery representation in suitable situations.
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