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Categorical and Floer-theoretic entropies: comparison and counting conjugacy classes in symplectic mapping class groups

  • Sangjin Lee
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Abstract

Let W be a Weinstein manifold and let f: W → W be a compactly supported symplectic automorphism. Using Floer theories, one can define two different entropies of f, called "Floer-theoretic" entropy and "categorical" entropy. The current article compares these two entropies and show that the former bounds the latter from below. As an application of the comparison, using that these entropies are invariants up to the conjugate relation, we count conjugacy classes in symplectic mapping classes. Especially, we show an exponential abundance of conjugacy classes that are smoothly isotopic to the identity, when W is a Weinstein manifold of dimension 4n ≥ 6, satisfying a local condition.

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Cite

BibTeXRIS
BibTeX
@misc{lee2026categorical,
  title = {{Categorical and Floer-theoretic entropies: comparison and counting conjugacy classes in symplectic mapping class groups}},
  author = {Sangjin Lee},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04161},
  eprint = {2611.04161},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04161},
}
RIS
TY  - UNPB
TI  - Categorical and Floer-theoretic entropies: comparison and counting conjugacy classes in symplectic mapping class groups
AU  - Sangjin Lee
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04161
UR  - https://arxiv.org/abs/2611.04161
AB  - Let W be a Weinstein manifold and let f: W → W be a compactly supported symplectic automorphism. Using Floer theories, one can define two different entropies of f, called "Floer-theoretic" entropy and "categorical" entropy. The current article compares these two entropies and show that the former bounds the latter from below. As an application of the comparison, using that these entropies are invariants up to the conjugate relation, we count conjugacy classes in symplectic mapping classes. Especially, we show an exponential abundance of conjugacy classes that are smoothly isotopic to the identity, when W is a Weinstein manifold of dimension 4n ≥ 6, satisfying a local condition.
ER  -