Fibrations with Legendrian Fibers
Tamas Kalman (Tam\'{a}s K\'{a}lm\'{a}n)
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I will consider contact $3$--manifolds
$(M,\xi)$ that are also total spaces of fibrations with a two-dimensional base $F$, so that the fibers are Legendrian with respect to $\xi$. A Legendrian knot $K$ in $M$ then has a front projection to $F$. I will show how, for a fixed base $F$ with standard constant curvature metric, $M=ST^*F$ (the bundle of cooriented contact elements to $F$) and $K$, one can vary the fibration so that the resulting family of projections is a wave propagation. I will also prove that if the fiber is a circle, then $M$ is a covering space of $PT^*F$, the bundle of contact elements to $F$.
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