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PreprintCC BY 4.0arXiv

Floer-theoretic entropy of exact symplectomorphisms

  • Joontae Kim
  • Myeonggi Kwon
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Abstract

We introduce the notion of a Penner-type class of an exact symplectomorphism on a Liouville domain with an Ak-configuration of Lagrangian spheres for kgeqslant 2, and prove that such a class has positive Floer-theoretic entropy. As a corollary, we construct infinitely many smoothly trivial symplectic isotopy classes of exact symplectomorphisms with positive Floer-theoretic entropy on any 4n-dimensional Liouville domain that admits an A2-configuration of Lagrangian spheres. We also prove that the Floer-theoretic entropy of an exact symplectomorphism on a Liouville domain provides a lower bound for its topological entropy.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026floertheoretic,
  title = {{Floer-theoretic entropy of exact symplectomorphisms}},
  author = {Joontae Kim and Myeonggi Kwon},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.21780},
  eprint = {2608.21780},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.21780},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Floer-theoretic entropy of exact symplectomorphisms
AU  - Joontae Kim
AU  - Myeonggi Kwon
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.21780
UR  - https://arxiv.org/abs/2608.21780
AB  - We introduce the notion of a Penner-type class of an exact symplectomorphism on a Liouville domain with an A_k-configuration of Lagrangian spheres for kgeqslant 2, and prove that such a class has positive Floer-theoretic entropy. As a corollary, we construct infinitely many smoothly trivial symplectic isotopy classes of exact symplectomorphisms with positive Floer-theoretic entropy on any 4n-dimensional Liouville domain that admits an A_2-configuration of Lagrangian spheres. We also prove that the Floer-theoretic entropy of an exact symplectomorphism on a Liouville domain provides a lower bound for its topological entropy.
ER  -