Hamiltonian circle actions on eight-dimensional manifolds with minimal fixed sets

D. Jang, S. Tolman

Research output: Contribution to journalArticlepeer-review


Let the circle act in a Hamiltonian fashion on a closed 8-dimensional sym-plectic manifold M with exactly five fixed points, which is the smallest possible fixed set. In [GS], L. Godinho and S. Sabatini show that if M satisfies an extra “positivity condition” then the isotropy weights at the fixed points of M agree with those of some linear action on ℂℙ 4. As a consequence, H *(M; ℤ) = ℤ[y]/y 5 and c(TM) = (1 + y) 5. In this paper, we prove that their positivity condition holds for M. This completes the proof of the “symplectic Petrie conjecture” for Hamiltonian circle actions on 8-dimensional closed symplectic manifolds with minimal fixed sets.

Original languageEnglish (US)
Pages (from-to)353-359
Number of pages7
JournalTransformation Groups
Issue number2
StatePublished - Jun 1 2017

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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