Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules

By L. Polterovich, E. Shelukhin. 2014

120 citations recorded by the source corpus.

We find robust obstructions to representing a Hamiltonian diffeomorphism as a full k-th power, $$k \ge 2$$k≥2, and in particular, to including it into a one-parameter subgroup. The robustness is understood in the sense of Hofer’s metric. Our approach is based on the theory of persistence modules applied in the context of filtered Floer homology. We present applications to geometry and dynamics of Hamiltonian diffeomorphisms.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5553571db6be7144ef7e413afefd01557c824e3a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. P. Seidel

In Geometry and Topology

1. P. Seidel
2. D. Auroux
3. M. Abouzaid
4. I. Smith
5. Alexander F. Ritter
6. Frederick J. Bourgeois III
7. Mark McLean
8. A. Oancea

In Mathematical Physics

1. P. Seidel
2. D. Auroux
3. M. Abouzaid
4. I. Smith
5. Alexander F. Ritter
6. Mark McLean
7. A. Oancea
8. Frederick J. Bourgeois III

Citations in the corpus

• Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, background): “There is a related situation where fixed point Floer cohomology admits a discrete symmetry, which was extensively studied in [46, 35].”