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

We present the first examples of elements in the fundamental group of thespace of Legendrian links in the standard contact 3-sphere whose action on theLegendrian contact DGA is of infinite order. This allows us to construct thefirst families of Legendrian links that can be shown to admit infinitely manyLagrangian fillings by Floer-theoretic techniques. These families include thefirst known Legendrian links with infinitely many fillings that are not rainbowclosures of positive braids, and the smallest Legendrian link with infinitelymany fillings known to date. We discuss how to use our examples to constructother links with infinitely many fillings, in particular giving the firstFloer-theoretic proof that Legendrian (n,m) torus links have infinitely manyLagrangian fillings, if n is greater than 3 and m greater than 6, or(n,m)=(4,4),(4,5). In addition, for any given higher genus, we construct aWeinstein 4-manifold homotopic to the 2-sphere whose wrapped Fukaya categorycan distinguish infinitely many exact closed Lagrangian surfaces of that genus.A key technical ingredient behind our results is a new combinatorial formulafor decomposable cobordism maps between Legendrian contact DGAs with integer(group ring) coefficients.

Braid Loops with infinite monodromy on the Legendrian contact DGA