Topologically Distinct Lagrangian and Symplectic Fillings

Abstract

We construct infinitely many Legendrian links in the standard contact ${\mathbb{R}}^3$ with arbitrarily many topologically distinct Lagrangian fillings. The construction is used to find links in $S^3$ that bound topologically distinct pieces of algebraic curves in $B^4\subset {\mathbb{C}}^2$, is applied to find contact 3-manifolds with topologically distinct symplectic fillings, and is generalized to higher dimensions.

16 pages, 8 figures

References in corpus (6)

• Algebraic functions and closed braids
• Legendrian Ambient Surgery and Legendrian Contact Homology
• Lifting pseudo-holomorphic polygons to the symplectisation of $P\times \mathbb{R}$ and applications
• Generating family invariants for Legendrian links of unknots
• A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}
• Some non-collarable slices of Lagrangian surfaces