English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we construct a 2-functor from the unobstructed immersedWeinstein category to the category of all filtered A infinity categories. Weconsider arbitrary (compact) symplectic manifolds and its arbitrary (relativelyspin) immersed Lagrangian submanifolds. The filtered A infinity categoryassociated to a symplectic manifold is defined by using Lagrangian Floer theoryin such generality by Fukaya-Oh-Ohta-Ono and Akaho-Joyce. The morphism ofunobstructed immersed Weinstein category is by definition a pair of immersedLagrangian submanifold of the direct product and its bounding cochain (in thesense of Fukaya-Oh-Ohta-Ono and Akaho-Joyce). Such a morphism transforms an(immersed) Lagrangian submanifold of one factor to one of the other factor. Thekey new result proved in this paper shows that this geometric transformationpreserves unobstructed-ness of the Lagrangian Floer theory. Thus, this papergeneralizes earlier results by Wehrheim-Woodward and Mau's-Wehrheim-Woodward sothat it works in complete generality in the compact case. The main idea of theproofs are based on Lekili-Lipiyansky's Y diagram and a lemma from homologicalalgebra, together with systematic use of Yoneda functor. In other words theproofs are based on a different idea from those which are studied byBottmann-Mau's-Wehrheim-Woodward, where strip shrinking and figure 8 bubbleplays the central role.

Unobstructed immersed Lagrangian correspondence and filtered A infinity functor