TY - JOUR
T1 - Hamiltonian circle actions on eight-dimensional manifolds with minimal fixed sets
AU - Jang, D.
AU - Tolman, S.
N1 - Funding Information:
∗Donghoon Jang is partially supported by Campus Research Board University of Illinois at Urbana–Champaign. ∗∗Susan Tolman is partially supported by NSF Grant DMS #12-06365. Received April 17, 2015. Accepted February 10, 2016. Published online March 19, 2016. Corresponding Author: D. Jang, e-mail: [email protected].
PY - 2017/6/1
Y1 - 2017/6/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00031-016-9370-0
DO - 10.1007/s00031-016-9370-0
M3 - Article
SN - 1083-4362
VL - 22
SP - 353
EP - 359
JO - Transformation Groups
JF - Transformation Groups
IS - 2
ER -