Séminaire Géométrie Topologie Dynamique
Lagrangian Hofer metric and barcodes
30
nov. 2023
nov. 2023
Intervenant : | Patricia Dietzsch |
Institution : | ETH Zurich |
Heure : | 14h00 - 15h00 |
Lieu : | 2L8 |
A major tool in symplectic topology to study Lagrangian submanifolds are Lagrangian Floer homology groups. A richer algebraic invariant can be obtained using filtered Lagrangian Floer theory. The resulting object is a persistence module, giving rise to a barcode, whose bar lengths are invariants for pairs of Lagrangians. It is well-known that these numbers are lower bounds of the Lagrangian Hofer distance between the two Lagrangians.
In this talk we will discuss a reverse inequality: We will show an upper bound of the Lagrangian Hofer distance between equators in the cylinder in terms of a weighted sum of the lengths of the finite bars and the spectral distance.