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PreprintCC BY 4.0arXiv

Floer theory on based loops and fundamental groups of Lagrangians in ℂn

  • Shuhao Li
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Abstract

We obtain new constraints on the topology of Lagrangian submanifolds in the standard symplectic vector space ℂn using Floer theory on the based loop space, generalizing a theorem of Fukaya-Irie. In particular, we show that non-trivial connected sums of closed, spin, aspherical manifolds of even dimensions do not admit Lagrangian embeddings into ℂn. A feature of the proof is that the obstructedness of the Floer theory is used to constrain the fundamental group of the Lagrangian.

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Cite

BibTeXRIS
BibTeX
@misc{li2026floer,
  title = {{Floer theory on based loops and fundamental groups of Lagrangians in $\mathbbC^n$}},
  author = {Shuhao Li},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06574},
  eprint = {2611.06574},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06574},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Floer theory on based loops and fundamental groups of Lagrangians in ℂ^n
AU  - Shuhao Li
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06574
UR  - https://arxiv.org/abs/2611.06574
AB  - We obtain new constraints on the topology of Lagrangian submanifolds in the standard symplectic vector space ℂ^n using Floer theory on the based loop space, generalizing a theorem of Fukaya-Irie. In particular, we show that non-trivial connected sums of closed, spin, aspherical manifolds of even dimensions do not admit Lagrangian embeddings into ℂ^n. A feature of the proof is that the obstructedness of the Floer theory is used to constrain the fundamental group of the Lagrangian.
ER  -