221 research outputs found
Unlinking and unknottedness of monotone Lagrangian submanifolds
Under certain topological assumptions, we show that two monotone Lagrangian
submanifolds embedded in the standard symplectic vector space with the same
monotonicity constant cannot link one another and that, individually, their
smooth knot type is determined entirely by the homotopy theoretic data which
classifies the underlying Lagrangian immersion. The topological assumptions are
satisfied by a large class of manifolds which are realised as monotone
Lagrangians, including tori. After some additional homotopy theoretic
calculations, we deduce that all monotone Lagrangian tori in the symplectic
vector space of odd complex dimension at least five are smoothly isotopic.Comment: 31 page
The persistence of the Chekanov-Eliashberg algebra
We apply the barcodes of persistent homology theory to the
Chekanov-Eliashberg algebra of a Legendrian submanifold to deduce displacement
energy bounds for arbitrary Legendrians. We do not require the full
Chekanov-Eliashberg algebra to admit an augmentation as we linearize the
algebra only below a certain action level. As an application we show that it is
not possible to -approximate a stabilized Legendrian by a Legendrian that
admits an augmentation.Comment: 29 pages, 4 figures; version accepted for publication in Selecta
Mathematica. This is a major revision with many fixes and improvements. The
constant in Theorem 1.1 has been improved. The theory of barcodes have been
properly introduced in the new Section 2 together with new related
terminology. The proof of Theorem 1.1 was rewritten in the new language and
given a greater level of detail
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