Nearby Special Lagrangians
Mohammed Abouzaid, Yohsuke Imagi

TL;DR
This paper investigates the local structure of special Lagrangian submanifolds near a given one in a Calabi--Yau manifold, establishing conditions under which nearby special Lagrangians are close or cover the original.
Contribution
It provides new results on the local uniqueness and covering properties of special Lagrangians based on fundamental group conditions.
Findings
If $\pi_1Q$ is abelian, nearby special Lagrangians are $C^1$ close.
If $\pi_1Q$ is virtually solvable, nearby special Lagrangians of bounded degree are unbranched coverings.
Stronger results hold when $\pi_1Q$ is finite; weaker when it has no non-abelian free subgroups.
Abstract
Let be a Calabi--Yau manifold and a closed connected embedded special Lagrangian; closed Lagrangians mean compact Lagrangian submanifolds without boundary. We prove that if the fundamental group is abelian then there exists a Weinstein neighbourhood of in which every closed irreducibly immersed special Lagrangian with unobstructed Floer cohomology is close to We prove also that if is virtually solvable then for every positive integer there exists a Weinstein neighbourhood of in which every closed irreducibly immersed special Lagrangian of degree and with unobstructed Floer cohomology is unbranched; that is, the projection is a covering map. We prove a stronger statement when is finite and a weaker statement when has no non-abelian free subgroups. The conditions, the…
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Taxonomy
TopicsNonlinear Waves and Solitons · Mathematics and Applications · Control and Dynamics of Mobile Robots
