Mathematics – Symplectic Geometry
Scientific paper
2008-07-27
Mathematics
Symplectic Geometry
Revised version, to appear in Journal of Topology. Following referee suggestions, parts of sections 4 and 6 have been removed
Scientific paper
We show that if a Legendrian knot in standard contact ${\bb R}^3$ possesses a generating family then there exists an augmentation of the Chekanov-Eliashberg DGA so that the associated linearized contact homology (LCH) is isomorphic to singular homology groups arising from the generating family. In this setting we show Sabloff's duality result for LCH may be viewed as Alexander duality. In addition, we provide an explicit construction of a generating family for a front diagram with graded normal ruling and give a new approach to augmentation $\Rightarrow$ normal ruling.
Fuchs Dmitry
Rutherford Dan
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