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Relative symplectic cohomology in complex projective spaces

  • Adi Dickstein
  • Yaniv Ganor
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Abstract

Relative symplectic cohomology is an invariant of compact subsets of a closed symplectic manifold, introduced by Varolgunes. There are many examples of computations of this invariant over the Novikov field, but the collection of computed examples over the Novikov ring is still quite limited. One reason for this is that such computations require determining the relevant Floer complexes for Hamiltonians that are not necessarily C2-small Morse functions. In this work, we present a computation of relative symplectic cohomology over the Novikov ring for balls and their complements in ℂPn. Our computation relies on explicit descriptions of Floer complexes, in the Morse--Bott setting with cascades, for J-shaped Hamiltonians on ℂPn. This allows us to deduce new estimates for the stable displacement energy of the boundaries of balls in ℂPn.

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Cite

BibTeXRIS
BibTeX
@misc{dickstein2026relative,
  title = {{Relative symplectic cohomology in complex projective spaces}},
  author = {Adi Dickstein and Yaniv Ganor},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.17370},
  eprint = {2606.17370},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.17370},
}
RIS
TY  - UNPB
TI  - Relative symplectic cohomology in complex projective spaces
AU  - Adi Dickstein
AU  - Yaniv Ganor
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2606.17370
UR  - https://arxiv.org/abs/2606.17370
AB  - Relative symplectic cohomology is an invariant of compact subsets of a closed symplectic manifold, introduced by Varolgunes. There are many examples of computations of this invariant over the Novikov field, but the collection of computed examples over the Novikov ring is still quite limited. One reason for this is that such computations require determining the relevant Floer complexes for Hamiltonians that are not necessarily C^2-small Morse functions. In this work, we present a computation of relative symplectic cohomology over the Novikov ring for balls and their complements in ℂP^n. Our computation relies on explicit descriptions of Floer complexes, in the Morse--Bott setting with cascades, for J-shaped Hamiltonians on ℂP^n. This allows us to deduce new estimates for the stable displacement energy of the boundaries of balls in ℂP^n.
ER  -